Percentage — Exercise 10(C)

In a class test, the marks were awarded out of 80. Kamal obtained 65% marks. How many marks did he get?

Answer

Maximum marks = 80.

Marks obtained by Kamal = 65% of 80

$= \dfrac{65}{100} \times 80\\[1em] = \dfrac{5200}{100}\\[1em] = 52$

Hence, Kamal got 52 marks.

In an examination, Renu obtained 480 marks out of 750. What percentage of marks did she get?

Answer

Marks obtained by Renu = 480 and maximum marks = 750.

Percentage of marks obtained = $\left(\dfrac{480}{750} \times 100\right)$%

$= \dfrac{48000}{750}$%

= 64%

Hence, Renu got 64% marks.

In her annual examination Geeta scored 39 marks out of 60 in English and 51 out of 75 in Hindi. In which subject her performance was better?

Answer

Percentage of marks in English = $\left(\dfrac{39}{60} \times 100\right)$%

$= \dfrac{3900}{60}$%

= 65%

Percentage of marks in Hindi = $\left(\dfrac{51}{75} \times 100\right)$%

$= \dfrac{5100}{75}$%

= 68%

Since 68% > 65%, her performance in Hindi was better than in English.

Hence, Geeta's performance was better in Hindi.

In an examination, 640 students appeared. Of them, 544 passed and the rest failed. What percentage of the students failed?

Answer

Total number of students = 640.

Number of students who passed = 544.

Number of students who failed = 640 − 544 = 96.

Percentage of students who failed = $\left(\dfrac{96}{640} \times 100\right)$%

$= \dfrac{9600}{640}$%

= 15%

Hence, 15% of the students failed.

In an examination 1360 students appeared. Of them, 85% passed. How many students failed?

Answer

Total number of students = 1360.

Percentage of students who passed = 85%.

Percentage of students who failed = (100 − 85)% = 15%.

Number of students who failed = 15% of 1360

$= \dfrac{15}{100} \times 1360\\[1em] = \dfrac{20400}{100}\\[1em] = 204$

Hence, 204 students failed.

In an examination, a student has to secure 48% marks to pass. If Rahul gets 247 marks and fails by 5 marks, what are the maximum marks?

Answer

Marks obtained by Rahul = 247.

Since Rahul fails by 5 marks,

Pass marks = 247 + 5 = 252.

∴ 48% of maximum marks = 252

$\Rightarrow \dfrac{48}{100} \times \text{(maximum marks)} = 252\\[1em] \Rightarrow \text{Maximum marks} = \dfrac{252 \times 100}{48}\\[1em] \Rightarrow \text{Maximum marks} = \dfrac{25200}{48}\\[1em] \Rightarrow \text{Maximum marks} = 525$

Hence, the maximum marks are 525.

On a particular day, 96% of the students were present in a school. If the number of absentees on that day was 82, find the total strength of the school.

Answer

Percentage of students present = 96%.

Percentage of absentees = (100 − 96)% = 4%.

∴ 4% of total strength = 82

$\Rightarrow \dfrac{4}{100} \times \text{(total strength)} = 82\\[1em] \Rightarrow \text{Total strength} = \dfrac{82 \times 100}{4}\\[1em] \Rightarrow \text{Total strength} = \dfrac{8200}{4}\\[1em] \Rightarrow \text{Total strength} = 2050$

Hence, the total strength of the school is 2050.

The population of a town has increased by 5% in a year. Last year its population was 20320. What is the present population of the town?

Answer

Last year's population = 20320.

Increase in population = 5% of 20320

$= \dfrac{5}{100} \times 20320\\[1em] = \dfrac{101600}{100}\\[1em] = 1016$

Present population = (last year's population + increase)

= 20320 + 1016

= 21336

Hence, the present population of the town is 21336.

The price of a bat was ₹ 650. Now, its price has been increased by 6%. What is the increased price of the bat?

Answer

Original price of the bat = ₹ 650.

Increase in its price = 6% of ₹ 650

$= \dfrac{6}{100} \times 650\\[1em] = \dfrac{3900}{100}\\[1em] = ₹\ 39$

Increased price = (original price + increase)

= ₹ (650 + 39)

= ₹ 689

Hence, the increased price of the bat is ₹ 689.

The price of a cooler during last summer was quoted at ₹ 7250. In off season, the price has been reduced by 12%. What is the reduced price of the cooler?

Answer

Original price of the cooler = ₹ 7250.

Reduction in price = 12% of ₹ 7250

$= \dfrac{12}{100} \times 7250\\[1em] = \dfrac{87000}{100}\\[1em] = ₹\ 870$

Reduced price = (original price − reduction)

= ₹ (7250 − 870)

= ₹ 6380

Hence, the reduced price of the cooler is ₹ 6380.

The value of a car depreciates (decreases) by 10% every year. If the value of the new car is ₹ 225000, what will be its value after one year?

Answer

Value of the new car = ₹ 225000.

Depreciation in one year = 10% of ₹ 225000

$= \dfrac{10}{100} \times 225000\\[1em] = \dfrac{2250000}{100}\\[1em] = ₹\ 22500$

Value after one year = (original value − depreciation)

= ₹ (225000 − 22500)

= ₹ 202500

Hence, the value of the car after one year will be ₹ 202500.

Ashish is 175 cm tall. His sister Annu is 8% shorter than him. What is Annu's height?

Answer

Height of Ashish = 175 cm.

Annu is 8% shorter than Ashish.

Difference in height = 8% of 175 cm

$= \dfrac{8}{100} \times 175\\[1em] = \dfrac{1400}{100}\\[1em] = 14 \text{ cm}$

Annu's height = (175 − 14) cm = 161 cm

Hence, Annu's height is 161 cm.

An alloy consists of copper and zinc. It contains 60% copper and the rest is zinc. Find the quantity of copper and zinc in 425 g of this alloy.

Answer

Percentage of copper in the alloy = 60%.

Percentage of zinc in the alloy = (100 − 60)% = 40%.

Quantity of copper in 425 g of alloy = 60% of 425 g

$= \dfrac{60}{100} \times 425\\[1em] = \dfrac{25500}{100}\\[1em] = 255 \text{ g}$

Quantity of zinc in 425 g of alloy = 40% of 425 g

$= \dfrac{40}{100} \times 425\\[1em] = \dfrac{17000}{100}\\[1em] = 170 \text{ g}$

Hence, 425 g of the alloy contains 255 g of copper and 170 g of zinc.

A tin contained 25 litres of oil. Due to leakage 2 litres of oil was lost. What percentage of oil is still there in the tin?

Answer

Total oil in the tin = 25 litres.

Oil lost due to leakage = 2 litres.

Oil left in the tin = (25 − 2) litres = 23 litres.

Percentage of oil still there in the tin = $\left(\dfrac{23}{25} \times 100\right)$%

$= \dfrac{2300}{25}$%

= 92%

Hence, 92% of the oil is still there in the tin.

An election was contested by two candidates A and B. In all there were 25000 voters. 80% of the votes were polled. If A got 60% of the total votes polled, how many votes did B get?

Answer

Total number of voters = 25000.

Number of votes polled = 80% of 25000

$= \dfrac{80}{100} \times 25000\\[1em] = \dfrac{2000000}{100}\\[1em] = 20000$

Votes got by A = 60% of the total votes polled = 60% of 20000

$= \dfrac{60}{100} \times 20000\\[1em] = \dfrac{1200000}{100}\\[1em] = 12000$

Votes got by B = (votes polled − votes got by A)

= 20000 − 12000

= 8000

Hence, B got 8000 votes.

Mr Mehta had ₹ 60000. Out of this money, he gave 20% to his daughter, 35% to his son, 30% to his wife and the rest he donated to a Charitable Trust. How much did he donate?

Answer

Total money with Mr Mehta = ₹ 60000.

Percentage of money given to daughter, son and wife = (20 + 35 + 30)% = 85%.

Percentage of money donated = (100 − 85)% = 15%.

Money donated = 15% of ₹ 60000

$= \dfrac{15}{100} \times 60000\\[1em] = \dfrac{900000}{100}\\[1em] = ₹\ 9000$

Hence, Mr Mehta donated ₹ 9000 to the Charitable Trust.