Percentage - Exercise 9(D)

$\dfrac{2}{5}$ expressed as a percentage is

1. 20%
2. 40%
3. 50%
4. 10%

Answer

Given:

Fraction = $\dfrac{2}{5}$

To convert a fraction to a percentage, multiply by 100.

Percentage = $\left( \dfrac{2}{5} \times 100 \right)$% = $(2 \times 20)$% = 40%

Hence, option 2 is the correct option.

The ratio 1 : 4 expressed as a percentage is

1. 10%
2. 20%
3. 25%
4. 40%

Answer

Given:

Ratio = 1 : 4

And

1 : 4 = $\dfrac{1}{4}$

Percentage = $\left( \dfrac{1}{4} \times 100 \right)$% = 25%

Hence, option 3 is the correct option.

$2\dfrac{1}{7}$% expressed as a fraction is

1. $\dfrac{3}{49}$

2. $\dfrac{6}{137}$

3. $\dfrac{3}{140}$

4. $\dfrac{5}{147}$

Answer

Given:

Percentage = $2\dfrac{1}{7}$%

$2\dfrac{1}{7}$% = $\dfrac{15}{7}$%.

To convert to a fraction, divide by 100:

$\dfrac{15}{7} \times \dfrac{1}{100} = \dfrac{15}{700} = \dfrac{3}{140}$

Hence, option 3 is the correct option.

If x% of 80 = 16, then the value of x is

1. 12
2. 16
3. 20
4. 24

Answer

Given:

x% of 80 = 16

$\Rightarrow \dfrac{x}{100} \times 80 = 16 \\[1em] \Rightarrow x = \dfrac{16 \times 100}{80} \\[1em] \Rightarrow x = \dfrac{16 \times 5}{4} \\[1em] \Rightarrow x = 4 \times 5 \\[1em] \Rightarrow x = 20$

Hence, option 3 is the correct option.

What per cent of a day is 27 minutes?

1. $1\dfrac{7}{8}$%

2. $2\dfrac{3}{8}$%

3. $3\dfrac{3}{4}$%

4. $2\dfrac{1}{4}$%

Answer

Given:

Part = 27 minutes

Total = 1 day = 24 hours

Convert day to minutes: 24 x 60 = 1440 minutes.

$\text {Percentage} = \left( \dfrac {\text{Part}}{\text{Total}} \times 100 \right)$%

$\left( \dfrac{27}{1440} \times 100 \right)$%

= $\dfrac{2700}{1440}$%

= $\dfrac{270}{144}$%

= $\dfrac{15}{8}$% $\quad$ [Dividing 270 and 144 by 18]

= $1\dfrac{7}{8}$%

Hence, option 1 is the correct option.

A number decreased by 15% gives 68. The number is

1. 85
2. 80
3. 75
4. 70

Answer

Decreased by 15% becomes 68.

Let the number be x.

The new number is what remains after 15% has been taken away from 100%.

85% of x = 68

$\dfrac{85}{100}x = 68 \\[1em] \Rightarrow x = \dfrac{68 \times 100}{85} \\[1em] \Rightarrow x = \dfrac{4 \times 100}{5} \quad \text{[Dividing 68 and 85 by 17]} \\[1em] \Rightarrow x = \dfrac{4 \times 20}{1} \quad \text{[Dividing 100 and 5 by 5]} \\[1em] \Rightarrow x = 80$

Hence, option 2 is the correct option.

A number increased by 25% gives 45. The number is

1. 30
2. 32
3. 35
4. 36

Answer

Given:

Increased by 25% becomes 45.

Let the number be x.

The new number is the total after adding 25% to 100%.

125% of x = 45

$\Rightarrow \dfrac{125}{100}x = 45 \\[1em] \Rightarrow x = \dfrac{45 \times 100}{125} \\[1em] \Rightarrow x = \dfrac{45 \times 4}{5} \quad \text{[Dividing 100 and 125 by 25]} \\[1em] \Rightarrow x = \dfrac{9 \times 4}{1} \quad \text{[Dividing 45 and 5 by 5]} \\[1em] \Rightarrow x = 36$

Hence, option 4 is the correct option.

After an increase of 15%, the salary of a person becomes ₹ 51750. His original salary was

1. ₹ 45000
2. ₹ 48000
3. ₹ 50000
4. ₹ 59500

Answer

Given:

Salary becomes ₹ 51750 after 15% increase.

Let original salary be x.

115% of x = ₹ 51750

$\Rightarrow \dfrac{115}{100}x = ₹ 51750 \\[1em] \Rightarrow x = ₹ \dfrac{51750 \times 100}{115} \\[1em] \Rightarrow x = ₹ \dfrac{51750 \times 20}{23} \quad \text{[Dividing 100 and 115 by 5]} \\[1em] \Rightarrow x = ₹ \dfrac{2250 \times 20}{1} \quad \text{[Dividing 51750 and 23 by 23]} \\[1em] \Rightarrow x = ₹ 45000$

Hence, option 1 is the correct option.

In an examination, 95% of the total examinees passed. If the number of failures was 36, how many examinees were there?

1. 540
2. 680
3. 720
4. 810

Answer

Given:

Passed = 95%

Failures = 36

Failure percentage = 100% - 95% = 5%.

Let total examinees be x.

5% of x = 36

$\Rightarrow\dfrac{5}{100}x = 36 \\[1em] \Rightarrow x = \dfrac{36 \times 100}{5} \\[1em] \Rightarrow x = \dfrac{36 \times 20}{1} \\[1em] \Rightarrow x = 720$

Hence, option 3 is the correct option.

The value of a machine depreciates 15% annually. If its present value is ₹ 51000, what was its value one year earlier?

1. ₹ 43350
2. ₹ 48650
3. ₹ 56000
4. ₹ 60000

Answer

Given:

Present value = ₹ 51000

Depreciation = 15%

Let the value one year ago be x.

Depreciation means the value is taken away from 100%: 100% - 15% = 85%

85% of x = 51000

$\Rightarrow \dfrac{85}{100}x = ₹ 51000 \\[1em] \Rightarrow x = \dfrac{51000 \times 100}{85} \\[1em] \Rightarrow x = 600 \times 100 \\[1em] \Rightarrow x = ₹ 60000$

Hence, option 4 is the correct option.

Fill in the blanks :

(i) Add 15% of 60 to 40. ...............

(ii) A student scored 32 marks out of 40 in Maths. Express this as a per cent. ...............

(iii) If 40% of the length of a cloth is 120 cm, what is the whole length of the cloth? ...............

(iv) What per cent of 2.8 kg is 980 g? ...............

(v) Express 0.74 as a per cent. ...............

Answer

(i) Add 15% of 60 to 40. 49

(ii) A student scored 32 marks out of 40 in Maths. Express this as a per cent.80%

(iii) If 40% of the length of a cloth is 120 cm, what is the whole length of the cloth? 300 cm

(iv) What per cent of 2.8 kg is 980 g? 35%

(v) Express 0.74 as a per cent. 74%

Explanation

(i) Given:

Original number = 40

Percentage to add = 15% of 60

Calculate 15% of 60:

$= \dfrac{15}{100} \times 60 \\[1em] = \dfrac{15}{5} \times 3 \\[1em] = \dfrac{3}{1} \times 3 \\[1em] = 9$

Add this to 40:

40 + 9 = 49

(ii) Given:

Scored = 32

Total = 40

$\text {Percentage}= \left( \dfrac{\text{Scored}}{\text{Total}} \times 100 \right)$%

$= \dfrac{32}{40} \times 100 \\[1em] = \dfrac{4}{5} \times 100 \\[1em] = \dfrac{4}{1} \times 20 \\[1em]$

= 80%

(iii) Given:

40% of length = 120 cm.

Let the whole length be x.

$\dfrac{40}{100} \times x = 120 \\[1em] \Rightarrow x = \dfrac{120 \times 100}{40} \\[1em] \Rightarrow x = 3 \times 100 \\[1em] \Rightarrow x = 300 \text{ cm}$

(iv) Given:

Part = 980 g

Total = 2.8 kg

Convert total to grams:

1 kg = 1000 grams

2.8 kg = 2.8 x 1000 g = 2800g

$\text {Percentage} = \left( \dfrac {\text{Part}}{\text{Total}} \times 100 \right)$%

= $\left( \dfrac{980}{2800} \times 100 \right)$%

= $\dfrac{980}{28}$%

= 35%

(v) Given:

Decimal = 0.74

To convert a decimal to a percentage, multiply by 100.

0.74 x 100 = 74%

Write true (T) or false (F) :

(i) $\dfrac{1}{4}$ can be expressed as 0.25%.

(ii) 1 : 5 expressed as a per cent is 20%.

(iii) 100% of 1 is 100 and 1% of 100 is 100.

(iv) 16% of ₹ 25 is ₹ 10.

(v) 18 marks out of 30 marks is more than 50 marks out of 80 marks.

Answer

(i) False
Reason — To express a fraction as a percentage, we multiply by 100.

$\dfrac{1}{4} \times 100 = 25$%.

0.25 is the decimal form, but as a percentage, it is 25% not 0.25%.

(ii) True
Reason — The ratio 1 : 5 is written as the fraction $\dfrac{1}{5}$.

Percentage = $\Big( \dfrac{1}{5} \times 100 \Big)$% = 20%.

(iii) False
Reason —

100% of 1 = $\dfrac{100}{100} \times 1 = 1$

1% of 100 = $\dfrac{1}{100} \times 100 = 1$

Neither calculation results in 100. So the statement is false.

(iv) False
Reason — 16% of ₹ 25

$= ₹ \Big(\dfrac{16}{100} \times 25\Big) \\[1em] = ₹ \dfrac{16}{4} \\[1em] = ₹ 4$

The value ₹ 10 is incorrect. So the statement is false.

(v) False
Reason — We must compare the percentages:

Percentage = $\Big(\dfrac {\text{Scored Marks}}{\text{Total Marks}} \times 100\Big)$%

Percentage of first score

= $\Big(\dfrac{18}{30} \times 100\Big)$%

= $\Big(\dfrac{18}{3} \times 10\Big)$%

= $\Big(\dfrac{6}{1} \times 10\Big)$%

= 60%

Percentage of second score

= $\Big(\dfrac{50}{80} \times 100\Big)$%

= $\Big(\dfrac{50}{4} \times 5\Big)$%

= $\Big(\dfrac{25}{2} \times 5\Big)$%

= $\dfrac{125}{2}$%

= 62.5%

Since 60% < 62.5%, the statement that the first is "more" is false.

Radhika is in the Chemistry Laboratory and is working on a practical. She mixed three salts A, B and C taking 150 gm of A and 300 gm each of B and C to prepare a mixture X.

(1) The percentage of salt A in mixture X is :

1. 15%
2. 20%
3. 25%
4. 30%

(2) By what percent is salt C more than salt A in mixture X ?

1. 50%
2. 100%
3. 150%
4. 200%

(3) Radhika added 250 gm of salt B to mixture X to prepare a new mixture Y. By what per cent did salt B increase ?

1. $63\dfrac{1}{3}$%

2. 75%

3. $83\dfrac{1}{3}$%

4. 121%

(4) The percentage of salt A in mixture Y is :

1. 15%

2. $17\dfrac{1}{2}$%

3. 20%

4. $22\dfrac{1}{2}$

Answer

Given:

Salt A = 150 gm

Salt B = 300 gm

Salt C = 300 gm

Total weight of Mixture X = 150 + 300 + 300 = 750 gm

(1)
$\text {Percentage} = \Big( \dfrac{\text{Salt A}}{\text{Total weight of Mixture X}} \times 100 \Big)$%

= $\Big( \dfrac{150}{750} \times 100 \Big)$%

= $\Big( \dfrac{1}{5} \times 100 \Big)$%

= 20%

Hence, option 2 is the correct option.

(2)

Difference = Salt C - Salt A

Substituting the values in above, we get:

Difference = 300 - 150 = 150 gm

$\text {Percentage} = \Big( \dfrac{\text{Difference}}{\text{Value of A}} \times 100 \Big)$%

= $\Big( \dfrac{150}{150} \times 100 \Big)$%

= 100%

Hence, option 2 is the correct option.

(3)

Original B = 300 gm

Amount added = 250 gm

$\text {Increase}$% = $\Big( \dfrac{\text{Added amount}}{\text{Original B}} \times 100 \Big)$%

= $\Big( \dfrac{250}{300} \times 100 \Big)$%

= $\dfrac{250}{3}$%

= $83\dfrac{1}{3}$%

Hence, option 3 is the correct option.

(4)

New total weight (Mixture Y) = 750 + 250 = 1000 gm

Weight of Salt A remains 150 gm

$\text {Percentage} = \Big( \dfrac{\text{Salt A}}{\text{Total Weight (Mixture Y)}} \times 100 \Big)$%

= $\Big( \dfrac{150}{1000} \times 100 \Big)$%

= $\Big( \dfrac{150}{10} \times 1 \Big)$%

= 15%

Hence, option 1 is the correct option.

Today is Eid. Ameena is very happy. Everyone in her family gave her a few coins in her bag. She now has 25 one rupee coins, 20 two rupee coins and 15 five rupee coins in her bag.

(1) The number of five rupee coins is what per cent of the total number of coins in the bag ?

1. 15%
2. 20%
3. 25%
4. 30%

(2) The value of two rupee coins is what per cent of the total value of coins in the bag ?

1. $4\dfrac{3}{4}$%

2. $33\dfrac{1}{3}$%

3. 32%

4. $28\dfrac{4}{7}$%

(3) The number of five rupee coins is what per cent less than that of two rupee coins ?

1. $17\dfrac{1}{2}$%

2. 20%

3. 25%

4. $33\dfrac{1}{3}$%

(4) The value of five rupee coins is what per cent more than that of two rupee coins?

1. 70%

2. $75\dfrac{1}{2}$%

3. 80%

4. $87\dfrac{1}{2}$%

Answer

Given:

₹ 1 coins: 25 (Value = 1 x ₹ 25 = ₹ 25)

₹ 2 coins: 20 (Value = 2 x ₹ 20 = ₹ 40)

₹ 5 coins: 15 (Value = 5 x ₹ 15 = ₹ 75)

Total number of coins = 25 + 20 + 15 = 60 coins

Total value of coins = 25 + 40 + 75 = ₹ 140

(1)
$\text {Percentage} = \Big( \dfrac{\text{Number of 5 rupee coins}}{\text{Total number of coins}} \times 100 \Big)$%

= $\Big( \dfrac{15}{60} \times 100 \Big)$%

= $\Big( \dfrac{1}{4} \times 100 \Big)$%

= 25%

Hence, option 3 is the correct option.

(2)
$\text {Percentage} = \Big( \dfrac{\text{Value of 2 rupee coins}}{\text{Total value of coins}} \times 100 \Big)$%

= $\Big( \dfrac{40}{140} \times 100 \Big)$%

= $\Big( \dfrac{2}{7} \times 100 \Big)$%

= $\Big( \dfrac{200}{7} \Big)$%

= $28\dfrac{4}{7}$%

Hence, option 4 is the correct option.

(3)

Difference in number = Number of ₹ 2 coins - Number of ₹ 5 coins

Substituting the values in above, we get:

Difference = 20 - 15 = 5

Percentage =

$\Big( \dfrac{\text{Difference in number}}{\text{Number of ₹ 2 coins}} \times 100 \Big)$%

$\Big( \dfrac{5}{20} \times 100 \Big)$%

= $\Big( \frac{1}{4} \times 100 \Big)$%

= 25%

Hence, option 3 is the correct option.

(4)

Difference in value = Value of ₹ 5 coins - Value of ₹ 2 coins

Substituting the values in above, we get:

Difference in value = ₹ 75 - ₹ 40 = ₹ 35

Percentage =

$\Big( \dfrac{\text{Difference in value}}{\text{Value of ₹ 2 coins}} \times 100 \Big)$%

= $\Big( \dfrac{35}{40} \times 100 \Big)$%

= $\Big( \dfrac{7}{8} \times 100 \Big)$%

= $\Big( \dfrac{7}{2} \times 25 \Big)$%

= $\Big( \dfrac{175}{2} \Big)$%

= 87.5%

= $87\dfrac{1}{2}$%

Hence, option 4 is the correct option.

Assertion: 1% of 100 is 1 and 100% of 1 is also 1.

Reason: x% = $\dfrac{x}{100}$ and x% of y = $\dfrac{xy}{100}$.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.

Answer

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Explanation

Assertion:

1% of 100 = $\dfrac{1}{100} \times 100 = 1$

100% of 1 = $\dfrac{100}{100} \times 1 = 1$

Both are true. So, Assertion is true.

Reason:

x% = $\dfrac{x}{100}$ and x% of y = $\dfrac{xy}{100}$.

This is the correct formula and directly explains the assertion.

Hence, option 1 is the correct option.

Assertion: A man travelled 60 km by car and 240 km by train. He travelled 20% of the journey by car and 80% of the journey by train.

Reason: Per cent change = $\dfrac{Actual\ change}{Original\ value} \times 100$.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.

Answer

Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

Explanation

Assertion:

Total distance = 60 km + 240 km = 300 km.

Car% = $\Big( \dfrac{\text{Distance travelled by car}}{\text{Total distance}} \times 100 \Big)$%

= $\Big(\dfrac{60}{300} \times 100\Big)$%

= $\Big(\dfrac{60}{3} \times 1\Big)$%

= 20%

Train% = $\Big( \dfrac{\text{Distance travelled by train}}{\text{Total distance}} \times 100 \Big)$%

= $\Big(\dfrac{240}{300} \times 100\Big)$%

= $\Big(\dfrac{240}{3} \times 1\Big)$%

= 80%

Both percentages match. So, Assertion is True.

This formula in Reason is correct for calculating percentage change (increase or decrease). Reason is True.

To prove the Assertion, we didn't use the formula for "Per cent change." We used the formula for "Part as a percentage of a whole." The Reason is a true statement, but it does not explain how we got the 20% and 80%.

Hence, option 2 is the correct option.

Assertion: If we multiply a number by $\dfrac{2}{5}$, it will increase by 20%.

Reason: Increase or decrease value is always calculated on the original value.

1. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
3. Assertion (A) is true but Reason (R) is false.
4. Assertion (A) is false but Reason (R) is true.

Answer

Assertion (A) is false but Reason (R) is true.

Explanation

Assertion:

Multiplying a number by $\dfrac{2}{5}$ is the same as multiplying by 0.4 (which is 40%).

If you multiply a number by 0.4, you are making it smaller (40% of its original size). To increase a number, the multiplier must be greater than 1.

An increase of 20% would mean multiplying by 1.20 or $\dfrac{6}{5}$.

Therefore, the statement is false. Assertion is False.

Reason:

Increase or decrease value is always calculated on the original value.

This is a fundamental rule of percentage applications. Reason is True.

Hence, option 4 is the correct option.

A sum of money was divided among three labourers — Dinesh, Prakash and Kamal in such a way that Dinesh gets 3 parts, Prakash gets 4 parts and Kamal gets 3 parts. The percentage share of Dinesh, Prakash, and Kamal respectively are:

1. 20%, 70%, 10%
2. 25%, 50%, 25%
3. 30%, 40%, 30%
4. 40%, 20%, 40%

Answer

Given:

Dinesh's share = 3 parts

Prakash's share = 4 parts

Kamal's share = 3 parts

Total parts = 3 + 4 + 3 = 10 parts

Dinesh's percentage =

$\left( \dfrac{\text{Dinesh's parts}}{\text{Total parts}} \times 100 \right)$%

= $\left( \dfrac{3}{10} \times 100 \right)$%

= $(3 \times 10)$%

= 30%

Prakash's percentage =

$\left( \dfrac{\text{Prakash's parts}}{\text{Total parts}} \times 100 \right)$%

= $\left( \dfrac{4}{10} \times 100 \right)$%

= $(4 \times 10)$%

= 40%

Kamal's percentage =

$\left( \dfrac{\text{Kamal's parts}}{\text{Total parts}} \times 100 \right)$%

= $\left( \dfrac{3}{10} \times 100 \right)$%

= $(3 \times 10)$%

= 30%

Hence, option 3 is the correct option.

A school team won 6 games this year against 4 games won last year. What is the per cent increase?

1. 10%
2. 25%
3. 75%
4. 50%

Answer

Given:

Games won last year = 4

Games won this year = 6

Increase in games won = This year - Last year

Substituting the values above, we get:

Increase in games won = 6 - 4 = 2

Increase % =

$\left( \dfrac{\text{Increase in games won}}{\text{Games won last year}} \times 100 \right)$%

= $\left( \dfrac{2}{4} \times 100 \right)$%

= $\left( \dfrac{1}{2} \times 100 \right)$%

= 50%

Hence, option 4 is the correct option.

If 55% of 1000 : 60% of 2000 = k : 2k + 2, then the value of k is:

1. 4
2. 5
3. 8
4. 11

Answer

Given:

55% of 1000 : 60% of 2000 = k : 2k + 2

First, calculate 55% of 1000:

55% of 1000 = $\dfrac{55}{100} \times 1000$

$= 55 \times 10 \\[1em] = 550$

Next, calculate 60% of 2000:

60% of 2000 = $\dfrac{60}{100} \times 2000$

$= 60 \times 20 \\[1em] = 1200$

So, the equation becomes:

550 : 1200 = k : (2k + 2)

Writing the ratios as fractions:

$\dfrac{550}{1200} = \dfrac{k}{2k + 2}$

By cross multiplying, we get:

$550 \times (2k + 2) = 1200 \times k \\[1em] \Rightarrow 1100k + 1100 = 1200k \\[1em] \Rightarrow 1200k - 1100k = 1100 \\[1em] \Rightarrow 100k = 1100 \\[1em] \Rightarrow k = \dfrac{1100}{100} \\[1em] \Rightarrow k = 11$

Hence, option 4 is the correct option.

The marks in a test decreased from 40 to 30. The percentage decrease is:

1. 10%
2. 20%
3. 25%
4. 40%

Answer

Given:

Original marks = 40

New marks = 30

Decrease in marks = Original marks - New marks

Substituting the values above, we get:

Decrease in marks = 40 - 30 = 10

Decrease % =

$\left( \dfrac{\text{Decrease in marks}}{\text{Original marks}} \times 100 \right)$%

= $\left( \dfrac{10}{40} \times 100 \right)$%

= $\left( \dfrac{1}{4} \times 100 \right)$%

= 25%

Hence, option 3 is the correct option.

Which of the following is greater than 16.3%?

1. 163 out of 1000
2. 113 out of 250
3. 8 out of 50
4. 39 out of 750

Answer

To find which option is greater than 16.3%, we convert each option into a percentage and compare.

(1) 163 out of 1000

= $\left( \dfrac{163}{1000} \times 100 \right)$%

= $\dfrac{163}{10}$%

= 16.3%

This is equal to 16.3%, not greater.

(2) 113 out of 250

= $\left( \dfrac{113}{250} \times 100 \right)$%

= $\left( \dfrac{113}{25} \times 10 \right)$%

= $\dfrac{1130}{25}$%

= 45.2%

This is greater than 16.3%.

(3) 8 out of 50

= $\left( \dfrac{8}{50} \times 100 \right)$%

= $(8 \times 2)$%

= 16%

This is less than 16.3%.

(4) 39 out of 750

= $\left( \dfrac{39}{750} \times 100 \right)$%

= $\left( \dfrac{39}{75} \times 10 \right)$%

= $\dfrac{390}{75}$%

= 5.2%

This is less than 16.3%.

Hence, option 2 is the correct option.

What percentage of the given figure is shaded?

1. 50%
2. 60%
3. 70%
4. 65%

Answer

From the figure, we observe:

Total number of squares = 36

Number of fully shaded squares = 12

Number of half shaded squares = 12

Half-shaded squares combine to make 6 full squares

Total number of shaded squares = 12 + 6 = 18

Percentage of shaded part =

$\left( \dfrac{\text{Number of shaded squares}}{\text{Total number of squares}} \times 100 \right)$%

= $\left( \dfrac{18}{36} \times 100 \right)$%

= $\left(\dfrac{1}{2} \times 100\right)$%

= 50%

Hence, option 1 is the correct option.

₹50 are to be divided between Mahima and Meenu. Mahima gets 60%. What does Meenu get?

1. ₹ 10
2. ₹ 20
3. ₹ 30
4. ₹ 40

Answer

Given:

Total amount = ₹ 50

Mahima's share = 60%

Meenu's share % = 100% - 60% = 40%

Meenu's amount =

40% of ₹ 50

$= ₹ \left( \dfrac{40}{100} \times 50 \right) \\[1em] = ₹ \left( \dfrac{40}{2} \times 1 \right) \\[1em] = ₹ 20$

Hence, option 2 is the correct option.

By how much is 80% of 40 greater than $\dfrac{4}{5}$ of 25?

1. 10
2. 12
3. 15
4. 18

Answer

First, calculate 80% of 40:

80% of 40 = $\dfrac{80}{100} \times 40$

$= \dfrac{80}{10} \times 4 \\[1em] = 8 \times 4 \\[1em] = 32$

Next, calculate $\dfrac{4}{5}$ of 25:

$\dfrac{4}{5} \text{ of } 25 = \dfrac{4}{5} \times 25 \\[1em] = 4 \times 5 \\[1em] = 20$

Difference = 80% of 40 - $\dfrac{4}{5}$ of 25

Substituting the values above, we get:

Difference = 32 - 20 = 12

Hence, option 2 is the correct option.

Surabhi's both parents are working. Her father's monthly salary is ₹ 40,000 and her mother's monthly salary is ₹ 24,000. Her father spends 50% of his salary and her mother spends 40% of her salary.

(i) Both the parents together spend 40% + 50% = 90% of their total monthly income.

(ii) Both the parents together save less than 50% of their total income.

1. Only (i) is correct
2. Only (ii) is correct
3. Both (i) and (ii) are correct
4. Both (i) and (ii) are wrong

Answer

Given:

Father's salary = ₹ 40,000

Mother's salary = ₹ 24,000

Father spends = 50% of his salary

Mother spends = 40% of her salary

Total monthly income = ₹ 40,000 + ₹ 24,000 = ₹ 64,000

Father's spending =

50% of ₹ 40,000

$= ₹ \left( \dfrac{50}{100} \times 40000 \right) \\[1em] = ₹ \left( \dfrac{1}{2} \times 40000 \right) \\[1em] = ₹ 20,000$

Mother's spending =

40% of ₹ 24,000

$= ₹ \left( \dfrac{40}{100} \times 24000 \right) \\[1em] = ₹ \left( \dfrac{2}{5} \times 24000 \right) \\[1em] = ₹ (2 \times 4800) \\[1em] = ₹ 9,600$

Total spending = ₹ 20,000 + ₹ 9,600 = ₹ 29,600

Total spending % =

$\left( \dfrac{\text{Total spending}}{\text{Total income}} \times 100 \right)$%

= $\left( \dfrac{29600}{64000} \times 100 \right)$%

= $\left( \dfrac{29600}{640} \right)$%

= $\dfrac{2960}{64}$%

= 46.25%

Checking statement (i):

Both parents together spend 46.25% of their total monthly income, not 90%. Percentages of different amounts cannot be simply added together because they are calculated on different bases (40000 and 24000).

So, statement (i) is wrong.

Total savings = Total income - Total spending

Total savings = ₹ 64,000 - ₹ 29,600 = ₹ 34,400

Percentage of total income saved =

$\left( \dfrac{\text{Total savings}}{\text{Total income}} \times 100 \right)$%

= $\left( \dfrac{34400}{64000} \times 100 \right)$%

= $\left( \dfrac{34400}{640} \right)$%

= $\dfrac{3440}{64}$%

= 53.75%

Checking statement (ii):

Both parents together save 53.75%, which is more than 50% of their total income.

So, statement (ii) is wrong.

Hence, option 4 is the correct option.

Kamajeet earned ₹ 1,00,000 per month. He used to spend 20% of his salary on food each month. Due to pandemic, his monthly salary was reduced by 20%. But his expenditure on food remained the same.

(i) He spends 25% of his new salary on food after the pandemic.

(ii) His reduced salary is ₹ 80,000.

1. Only (i) is correct
2. Only (ii) is correct
3. Both (i) and (ii) are correct
4. Both (i) and (ii) are wrong

Answer

Given:

Original salary = ₹ 1,00,000

Food expenditure = 20% of salary

Salary reduction = 20%

Food expenditure =

20% of ₹ 1,00,000

$= ₹ \left( \dfrac{20}{100} \times 100000 \right) \\[1em] = ₹ (20 \times 1000) \\[1em] = ₹ 20,000$

Salary reduction amount =

20% of ₹ 1,00,000

$= ₹ \left( \dfrac{20}{100} \times 100000 \right) \\[1em] = ₹ (20 \times 1000) \\[1em] = ₹ 20,000$

New salary = Original salary - Salary reduction

New salary = ₹ 1,00,000 - ₹ 20,000 = ₹ 80,000

Checking statement (ii):

His reduced salary is ₹ 80,000.

So, statement (ii) is correct.

Food expenditure remains the same at ₹ 20,000.

Percentage of new salary spent on food =

$\left( \dfrac{\text{Food expenditure}}{\text{New salary}} \times 100 \right)$%

= $\left( \dfrac{20000}{80000} \times 100 \right)$%

= $\left( \dfrac{1}{4} \times 100 \right)$%

= 25%

Checking statement (i):

He spends 25% of his new salary on food after the pandemic.

So, statement (i) is correct.

Hence, option 3 is the correct option.