Percentage — Competency Focused Questions

A product's price increases from ₹ 89.50 to ₹ 99.45. By what percentage (to 2 decimal places) did the price increase?

1. 12.12%

2. 11%

3. 11.12%

4. 12%

Answer

Original price = ₹ 89.50 and new price = ₹ 99.45.

Increase in price = ₹ (99.45 − 89.50) = ₹ 9.95.

Percentage increase = $\left(\dfrac{\text{Increase}}{\text{Original price}} \times 100\right)$%

$= \left(\dfrac{9.95}{89.50} \times 100\right)$%

$= \dfrac{995}{89.5}$%

= 11.12% (to 2 decimal places)

Hence, option 3 is the correct option.

A school survey shows the favourite subjects of students:

(i) 40% like Math

(ii) 30% like Science

(iii) 20% like English

(iv) 10% like Social Science

If 300 students participated in the survey, how many students like Math and Science combined?

1. 120

2. 200

3. 210

4. 270

Answer

Percentage of students who like Math and Science combined = (40 + 30)% = 70%.

Number of students who like Math and Science combined = 70% of 300

$= \dfrac{70}{100} \times 300\\[1em] = \dfrac{21000}{100}\\[1em] = 210$

Hence, option 3 is the correct option.

Two numbers are in the ratio 3 : 5. If 40% of the smaller number is 24, then 60% of the larger number is:

1. 50

2. 70

3. 80

4. 60

Answer

Let the two numbers be 3x and 5x. Then, the smaller number = 3x and the larger number = 5x.

40% of the smaller number = 24

$\Rightarrow \dfrac{40}{100} \times 3x = 24\\[1em] \Rightarrow \dfrac{120x}{100} = 24\\[1em] \Rightarrow x = \dfrac{24 \times 100}{120}\\[1em] \Rightarrow x = 20$

So, the larger number = 5x = 5 × 20 = 100.

60% of the larger number = 60% of 100

$= \dfrac{60}{100} \times 100$

= 60

Hence, option 4 is the correct option.

A rectangular garden is divided into four sections, and the percentages of the garden used for each purpose are:

Flowers: 30%, Vegetables: 25%, Grass: 35%, Trees: 10%

If the total area of the garden is 800 m², what is the area used for vegetables and flowers?

1. 440 m²

2. 200 m²

3. 400 m²

4. 480 m²

Answer

Percentage of the garden used for vegetables and flowers = (25 + 30)% = 55%.

Area used for vegetables and flowers = 55% of 800 m²

$= \dfrac{55}{100} \times 800\\[1em] = \dfrac{44000}{100}\\[1em] = 440 \text{ m}^2$

Hence, option 1 is the correct option.

A farmer's field produces wheat. 20% of the harvest is used for personal consumption, and 40% is sold to the market. The remaining 60 tonnes are stored. What was the total harvest of wheat?

1. 100 tonnes

2. 120 tonnes

3. 150 tonnes

4. 200 tonnes

Answer

Percentage of harvest used for personal consumption and sold to the market = (20 + 40)% = 60%.

Percentage of harvest stored = (100 − 60)% = 40%.

Let the total harvest be x tonnes.

40% of x = 60

$\Rightarrow \dfrac{40}{100} \times x = 60\\[1em] \Rightarrow x = \dfrac{60 \times 100}{40}\\[1em] \Rightarrow x = 150$

Hence, option 3 is the correct option.

75% of a number when added to 75 is equal to the number. The number is:

1. 600

2. 400

3. 300

4. 200

Answer

Let the required number be x.

75% of x + 75 = x

$\Rightarrow \dfrac{75}{100} \times x + 75 = x\\[1em] \Rightarrow \dfrac{3x}{4} + 75 = x\\[1em] \Rightarrow x - \dfrac{3x}{4} = 75\\[1em] \Rightarrow \dfrac{x}{4} = 75\\[1em] \Rightarrow x = 75 \times 4\\[1em] \Rightarrow x = 300$

Hence, option 3 is the correct option.

Ajay, Kapil and Varun are three friends studying in the same class. In a class test in Maths, Ajay got 40 out of 50, and Kapil got 36. The average score of the friends was 82%. In that test Varun scored:

1. 42 marks

2. 41 marks

3. 47 marks

4. 39 marks

Answer

The test was out of 50 marks.

Average score of the three friends = 82% of 50

$= \dfrac{82}{100} \times 50\\[1em] = \dfrac{4100}{100}\\[1em] = 41 \text{ marks}$

Total marks of the three friends = 41 × 3 = 123.

Marks of Ajay and Kapil = 40 + 36 = 76.

Marks scored by Varun = 123 − 76 = 47.

Hence, option 3 is the correct option.

Two alloys A and B contain gold and copper in the ratio 3 : 2 and 4 : 3 respectively. A 10 kg mixture is prepared by mixing equal quantities of A and B. What percentage of gold is present in the final mixture?

1. 57.58%

2. 58.57%

3. 60%

4. 56.55%

Answer

Since equal quantities of A and B are mixed to prepare 10 kg of mixture,

Quantity of alloy A = quantity of alloy B = 5 kg.

In alloy A, gold : copper = 3 : 2, so sum of ratio terms = 3 + 2 = 5.

Gold in 5 kg of alloy A = $\dfrac{3}{5} \times 5$ = 3 kg.

In alloy B, gold : copper = 4 : 3, so sum of ratio terms = 4 + 3 = 7.

Gold in 5 kg of alloy B = $\dfrac{4}{7} \times 5 = \dfrac{20}{7}$ kg.

Total gold in the mixture = $3 + \dfrac{20}{7} = \dfrac{21 + 20}{7} = \dfrac{41}{7}$ kg.

Percentage of gold in the final mixture = $\left(\dfrac{41}{7 \times 10} \times 100\right)$%

$= \dfrac{4100}{70}$%

$= \dfrac{410}{7}$%

= 58.57% (approx.)

Hence, option 2 is the correct option.