# QUESTIONS ON PERCENTAGE (PART-III)

## QUESTIONS ON PERCENTAGE (PART-III)

#### QUERY 21

**The ratio of numbers of boys and girls is 3:2. If 20% of the boys and 30% of the girls are scholarship holders, then the % of students who do not get scholarship is?**

A) 50%

B) 56%

C) 76%

D) 80%

**ANUJ YADAV**

Let number of boys = 3*100 = 300

And number of girls = 2*100 = 200

So, total students = 500

Hence number of boys getting scholarship = 300*20/100 = 60

And girls getting scholarship =200*30/100 = 60

Total student who get scholarship = 60+60 = 120

Not getting it = 500 – 120 = 380

Thus in percentage = (380/500)*100 = 76% (option ‘C’)

QUERY 22

**When water is changed into ice, its volume increases by 9%. If ice changes into water, the percentage decrease in volume is?**

A) 9%

B) 10%

C) 18%

D) 900/109 %

**MAHA GUPTA**

When water changes into ice, its volume increases by 9% means 100 becomes 109

When 109 of ice will change into water it will decrease by 109 – 100 = 9

If 100 of ice will change it will decrease by (9/100)*100 = 900/109

Hence 900/109% (option ‘D’) is the answer.

QUERY 23

**If the commission of an agent is increased from 4% to 5% but his income does not change, how much his business is affected in %?**

A) 20%

B) 25%

C) 22%

D) 30%

**MAHA GUPTA**

We must remember that the income of a commission agent is through commission only.

According to case-I his income is 4%, means income on Rs 100 is Rs 4

After the increase his income is 5%; means income on Rs 100 is Rs 5

But in actual his income remains the same i.e. Rs 4

So effect on income 5 – 4 = 1

Now effect on 5 = 1

Therefore effect on 100 = (1/5)*100 = 20 (option ‘A’)

QUERY 24

**A customer asks for the production of x number of goods. The company produces y number of goods daily out of which z% goods are unfit for sale. In how many days order will be completed?**

A) ^{200x}⁄_{[y(100 – z)]}

B) ^{100x}⁄_{[y(200 – z)]}

C) ^{100x}⁄_{[y(100 – z)]}

D) ^{150x}⁄_{[y(150 – z)]}

**MAHA GUPTA**

Number of days = ^{Demand}⁄_{supply}

Supply = y – z% of y = ^{(100y – yz)}⁄_{100}

So the number of days needed = ^{x}⁄_{[(100y – yz)/100)]}

= ^{100x}⁄_{[y(100 – z)]} (option ‘C’)

QUERY 25

**If a milkman sells milk at cost price but mixes water in it, he gains 25% on cost price. Then what will be the percentage of water in the mixture?**

A) 25%

B) 30%

C) 20%

D) 27%

**MAHA GUPTA**

Let the quantity of pure milk = 100 units

So selling price of the mixture of milk and water = cost price of 100 units of pure milk

But he gains 25% on cost price

So the quantity of pure milk in it = (^{100}⁄_{125})*100 = 80 units

Therefore quantity of water in the mixture = 100 – 80 = 20

In percentage quantity of water in the mixture = 20% (option ‘C’)

QUERY 26

**In the New York stock exchange there are 45% female employees and thus the number of male employees is exceeded by 72. Hence the total number of employees in the New York stock exchange is?**

A) 700

B) 720

C) 650

D) 800

**MAHA GUPTA**

Number of female employees = 45%

Means number of male employees = 100 – 45 = 55%

Hence difference in percentage = 55 – 45 = 10%

But the difference in number is = 72; means 72 is 10% of total

Therefore total number of employees = (^{100}⁄_{10})*72 = 720 (option ‘B’)

QUERY 27

**The salary of an employee of a company increases every month by 4%. If his salary in August was Rs.6300, what would be his approximate salary in the month of October in the same year?**

A) 6000

B) 7500

C) 6814

D) 7525

**MAHA GUPTA**

This is a case as we see in compound interest. But this is just a 2 month affair, we need not apply the formula meant for compound interest here as it’s a little time consuming. So better if it’s done applying simple approach. Look how:

Salary in the month of September = 6300 + 4% of 6300 = 6300 + 252 = 6552

Salary in October: 6552 + 4% of 6552 = 6552 + 262 .08 = 6814.08 = 6814 (approx) [option ‘C’]

QUERY 28

**A man invested 1/3 of his capital at 7% per annum, 1/4 at 8% per annum and the remainder at 10% per annum. If his annul income is Rs 561, the capital is?**

A) 6600

B) 6500

C) 7000

D) 7500

**MAHA GUPTA**

Let the capital be Rs 300

So his annual income on part-I = (^{300}⁄_{3})*(^{7}⁄_{100}) = 7

And income on part-II = (^{300}⁄_{4})*(^{8}⁄_{100}) = 6

Part-III = Total – (part-I + part-II) = 300 – (^{300}⁄_{3} + ^{300}⁄_{4}) = 125

So income on part-III = 125*(^{10}⁄_{100}) = 12.50

Hence the total income on Rs 300 = 7+6+12.50 = 25.50

Now, if the income is 25.50, the capital = 300

If income is 561, the capital = (^{300}⁄_{25.50})*561 = 6600 (option ‘A’)

QUERY 29

**Fresh grapes contain 80% water, while dry grapes contain 10% water. If the weight of dry grapes is 500 kg, what is is total weight when it is fresh?**

A) 2350 kg

B) 2085 kg

C) 2255 kg

D) 2250 kg

**MAHA GUPTA**

As dry grapes contain 10% water, therefore it has 90% pulp in it.

Fresh grapes contain 80% water, therefore it has 20% pulp in it.

Now Weight of Dry grapes = 500 kg

Letting total weight of fresh grapes x kg

Obviously the pulp in both the cases will be same

So, 90/100*500 = 20/100*x

=> 90*500 = 20x

=> x = 2250 kg (option ‘D’)

QUERY 30

**If fresh grapes contain 80% juice and 20% pulp, and dry grapes contain 90% pulp and 10% juice and of weight of dry grapes is 250 kg, then what will be the weight of fresh grapes?**

A) 1275 kg

B) 1045 kg

C) 1130 kg

D) 1125 kg

**MAHA GUPTA**

Dry grapes contain 10% juice and 90% pulp.

Fresh grapes contain 80% juice and 20% pulp.

Now Weight of Dry grapes = 250 kg

Letting total weight of fresh grapes x kg

Obviously the pulp in both the cases will be same

So, 90/100*250 = 20/100x

=> 90*250 = 20*x

=> x = 1125 kg (option ‘D’)