Percent and Percentage — Exercise 9(B)

Deepak bought a basket of mangoes containing 250 mangoes. 12% of these were found to be rotten. Of the remaining, 10% got crushed. How many mangoes were in good condition?

Answer

Total number of mangoes = 250.

Number of rotten mangoes = 12% of 250

$= \dfrac{12}{100} \times 250$

= 30

Remaining mangoes = 250 − 30 = 220.

Number of crushed mangoes = 10% of 220

$= \dfrac{10}{100} \times 220$

= 22

Mangoes in good condition = 220 − 22 = 198.

Hence, 198 mangoes were in good condition.

In a Maths Quiz of 60 questions, Chandra got 90% correct answers and Ram got 80% correct answers. How many correct answers did each give? What percent is Ram's correct answers to Chandra's correct answers?

Answer

Total number of questions = 60.

Chandra's correct answers = 90% of 60

$= \dfrac{90}{100} \times 60$

= 54

Ram's correct answers = 80% of 60

$= \dfrac{80}{100} \times 60$

= 48

Ram's correct answers as a percent of Chandra's = $\left(\dfrac{48}{54} \times 100\right)$%

$= \dfrac{4800}{54}$%

$= \dfrac{800}{9}$%

$= 88\dfrac{8}{9}$%

Hence, Chandra got 54 correct answers, Ram got 48 correct answers, and Ram's correct answers are $88\dfrac{8}{9}$% of Chandra's.

In an examination, the maximum marks are 900. A student gets 33% of the maximum marks and fails by 45 marks. What are the passing marks? Also, find the passing percentage.

Answer

Maximum marks = 900.

Marks obtained by the student = 33% of 900

$= \dfrac{33}{100} \times 900$

= 297

Since the student fails by 45 marks,

Passing marks = 297 + 45 = 342.

Passing percentage = $\left(\dfrac{342}{900} \times 100\right)$%

$= \dfrac{34200}{900}$%

= 38%

Hence, the passing marks = 342 and the passing percentage = 38%.

In a train, 15% people travel in first class and 35% travel in second class and the remaining travel in the A.C. class. Calculate the percentage of A.C. class travellers.

Answer

Percentage travelling in first class = 15%.

Percentage travelling in second class = 35%.

Percentage travelling in A.C. class = 100% − (15% + 35%)

= 100% − 50%

= 50%

Hence, the percentage of A.C. class travellers = 50%.

A boy eats 25% of the cake and gives away 35% of it to his friends. What percent of the cake is still left with him?

Answer

Percentage of cake eaten = 25%.

Percentage of cake given away = 35%.

Percentage of cake left = 100% − (25% + 35%)

= 100% − 60%

= 40%

Hence, 40% of the cake is still left with him.

What is the percentage of vowels in the English alphabet?

Answer

Total number of letters in the English alphabet = 26.

Number of vowels (a, e, i, o, u) = 5.

Percentage of vowels = $\left(\dfrac{5}{26} \times 100\right)$%

$= \dfrac{500}{26}$%

$= \dfrac{250}{13}$%

$= 19\dfrac{3}{13}$%

Hence, the percentage of vowels in the English alphabet = $19\dfrac{3}{13}$%.

$6\dfrac{1}{4}$% of what number is 375?

Answer

$6\dfrac{1}{4}$% = $\dfrac{25}{4}$%

Let the number be x whose $\dfrac{25}{4}$% = 375.

$\Rightarrow \dfrac{25}{4}$% of x = 375

$\Rightarrow \dfrac{25}{4}\times \dfrac{1}{100} \times x = 375\\[1em] \Rightarrow x = \dfrac{375 \times 400}{25}\\[1em] \Rightarrow x = 6000$

Hence, the required number = 6000.

0.2% of a number is 5. Find the number.

Answer

Let the number be x whose 0.2% = 5.

⇒ 0.2% of x = 5

$\Rightarrow \dfrac{0.2}{100} \times x = 5\\[1em] \Rightarrow x = \dfrac{5 \times 100}{0.2}\\[1em] \Rightarrow x = \dfrac{500}{0.2}\\[1em] \Rightarrow x = 2500$

Hence, the required number = 2500.

30 is $16\dfrac{2}{3}$% of a number. Find the number.

Answer

$16\dfrac{2}{3}$% = $\dfrac{50}{3}$%

Let the number be x whose $\dfrac{50}{3}$% = 30.

$\Rightarrow \dfrac{50}{3}$% of x = 30

$\Rightarrow \dfrac{50}{3} \times \dfrac{1}{100} \times x = 30\\[1em] \Rightarrow \dfrac{50}{300} \times x = 30\\[1em] \Rightarrow x = \dfrac{30 \times 300}{50}\\[1em] \Rightarrow x = 180$

Hence, the required number = 180.

The money spent on the repairs of a house was 1% of its value. If the repair costs ₹ 5,000, find the cost of the house.

Answer

Let the cost (value) of the house be ₹ x.

Given, 1% of its value = ₹ 5,000.

$\Rightarrow \dfrac{1}{100} \times x = 5,000\\[1em] \Rightarrow x = 5,000 \times 100\\[1em] \Rightarrow x = 5,00,000$

Hence, the cost of the house = ₹ 5,00,000.

In a school, out of 300 students, 70% are girls and 30% are boys. If 30 girls leave and no new student is admitted, what is the new percentage of girls in the school?

Answer

Total number of students = 300.

Number of girls = 70% of 300 = $\dfrac{70}{100} \times 300 = 210$.

Number of boys = 30% of 300 = $\dfrac{30}{100} \times 300 = 90$.

When 30 girls leave:

New number of girls = 210 − 30 = 180.

New total number of students = 300 − 30 = 270.

New percentage of girls = $\left(\dfrac{180}{270} \times 100\right)$%

$= \dfrac{18000}{270}$%

$= \dfrac{200}{3}$%

$= 66\dfrac{2}{3}$%

Hence, the new percentage of girls in the school = $66\dfrac{2}{3}$%.

Kumar bought a transistor for ₹ 960. He paid $12\dfrac{1}{2}$% cash money. The rest he agreed to pay in 12 equal monthly instalments. How much will he pay each month?

Answer

Cost of the transistor = ₹ 960.

$12\dfrac{1}{2}$% = $\dfrac{25}{2}$%

Cash money paid = $\dfrac{25}{2}$% of 960

$= \dfrac{25}{2} \times \dfrac{1}{100} \times 960\\[1em] = \dfrac{25 \times 960}{200}\\[1em] = ₹\ 120$

Remaining amount = 960 − 120 = ₹ 840.

Amount paid each month = $\dfrac{840}{12}$ = ₹ 70.

Hence, Kumar will pay ₹ 70 each month.

An ore contains 20% zinc. How many kg of ore will be required to get 45 kg of zinc?

Answer

Let the quantity of ore required be x kg.

Given, 20% of the ore = 45 kg of zinc.

$\Rightarrow \dfrac{20}{100} \times x = 45\\[1em] \Rightarrow x = \dfrac{45 \times 100}{20}\\[1em] \Rightarrow x = 225$

Hence, 225 kg of ore will be required.