# 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%

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 = Demandsupply

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 = (100125)*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 = (10010)*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 = (3003)*(7100) = 7
And income on part-II = (3004)*(8100) = 6

Part-III = Total – (part-I + part-II) = 300 – (3003 + 3004) = 125
So income on part-III = 125*(10100) = 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 = (30025.50)*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’)

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