QUESTIONS ON PERCENTAGE (PART-I)

QUERY 1

A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs 22500. What is the reduced price per kg of tea?

A) 90
B) 900
C) 80
D) 110

Amit jha
Reduction in the price 10%

Therefore the dealer’s saving due to this reduction = 10% of 22500 = 2250

Thus, now he’ll be able to buy 25 kg of tea in Rs 2250

Therefore the reduced price per kg = 2250/25 = Rs 90 per kg (option ‘A’)

 

QUERY 2

An increases of 20% in the price of mangoes enables a person to purchase 4 mangoes less for Rs 40. The price of 15 mangoes before increase was?

A) Rs 10
B) Rs 15
C) Rs 20
D) Rs 25

MAHA GUPTA
Person’s extra expenditure due to increase of 20% in price = 20% of 40 = Rs 8

Due this extra expenditure of Rs 8 the person is forced to buy 4 mangles less

Therefore the increased price per mango = 8/4 = Rs 2

Now, if increased price is 120 per mango the price before increase = 100
If increased price is Rs 2 per mango the price before increase = (100/120)*2 = 5/3

Hence Price for 15 mangoes before increase = (5/3)*15 = 25 (option ‘D’)

QUERY 3

The population of a town is 6000. In the next year if males increase by 8% and females by 10% the population is 6530. Find the number of males in the town.

A) 3500
B) 4500
C) 3200
D) 4000

Amit jha
Let N be the number of male
Therefore the number of female would be 6000 – N

Now increment in population is Male 8% and Female 10%
Thus new population = N × 108/100 + (6000 – N) × 110/100

So according to the question 108N/100 + (6000 – N) × 110/100 = 6530

=> 108 N + 660000 -110 N = 6530 × 100= 653000
Solving: N = 3500 i.e. the number of males (option ‘A’)

NOTE: For short cut … u can use hit and trial method..

QUERY 4

Entry fee in an exhibition was Re 1. Later this was reduced by 25% which increased the sale by 20 %. The percentage increase in the number of visitors is?

A) 54
B) 57
C) 60
D) 66

MAHA GUPTA
Let the total number of visitors before be 100
Therefore total sales before = 1*100 = 100
And the sale after reduction of price = 100 + 20% of 100 = 120 (Because the sale increased by 20%)

Now the price per ticket = 1 – 25% of 1 = Re 3/4
So the number of visitors now = Total sales/price per ticket = 120/(3/4) = 160

Thus the increase in the number of visitors over 100 = 160 – 100 = 60
Hence percent increase in the number of visitors = 60 (option ‘C’)

QUERY 5

There are three bottles of alcohol A, B and C with the capacity of 4, 5 and 1 litres respectively. A, B and C contain 45%, 48% and X% of alcohol respectively. From bottle C some alcohol is added to A and remaining to B. Both the bottles A and B now contain 50% alcohol. Find X

A) 63%
B) 70%
C) 80%
D) 30%

MAHA GUPTA
Alcohol BEFORE in bottle A = 45% of 4 liters = 1.8 liters
Alcohol AFTER in bottle A = 50% of 4 liters = 2 liters
Therefore transferred from bottle C = 2 – 1.8 = 0.2 liter

Alcohol BEFORE in bottle B = 48% of 5 liters = 2.4 liters
Alcohol AFTER in bottle B = 50% of 5 liters = 2.5 liters
Therefore transferred from bottle C = 2.5 – 2.4 = 0.1 liter

Thus total alcohol in bottle C = 0.2 + 0.1 = 0.3 liter
But this is x% of 1 liter i.e. x/100 liter

Hence x/100 = 0.3
=> x = 30 (option ‘D’)

QUERY 6

Suresh Kumar went to the market with Rs 100. If he buys three pens and six pencils he uses up all his money. On the other hand if he buys three pencils and six pens he would fall short by 20%. If he wants to buy equal number of pens and pencils, how many pencils can he buy?

A) 3
B) 4
C) 5
D) 6

MAHA GUPTA
The person is falling short of 20%, means Rs 100 is 80% of the total amount of his second transaction, i.e. the price of 6 pens and 3 pencils taken together.

Now let the total amount of that new transaction = x, therefore (80/100)*x = 100
=> x = 100*(100/80 = 125

And let the price per pen be Rs x and the price per pencil be Rs y

So according to the question now
3x + 6y = 100 and
6x + 3y = 125

solving the above x = 50/3, and y = 25/3
Hence the price of 1 pen and 1 pencil together = 75/3 = 25

Now we have to buy equal number of pens and pencil within the range of Rs 100
So he must be buying the number of pencils = 100/25 i.e. 4 (option ‘B’)

QUERY 7

845 people went zoo on Sunday and 169 people went zoo on Monday, what % decrease of visitor is on Sunday?

A) 60
B) 65
c) 70
D) 80

MAHA GUPTA
Decrease of visitors on Monday = 845 – 169 = 676

Decrease on 845 = 676
Therefore decrease on 100 = (676/845)*100 = 80 (option ‘D’)

QUERY 8

At a place married males are 25% and married females are 45%. Find the percentage of total persons.

A) 32.14
B) 32
C) 30.15
D) 35

MAHA GUPTA
Suppose the the number of males = 100
Then the number of married males = 25% of 100 = 25
Because a man can only be married to a woman (not cow, cat etc), the number of married females also is 25

But this is 45% of the married females; therefore number of females = (100/45)*25 = 500/9

Now the total number of males and females = 100 + 500/9 = 1400/9
Total number of married males and females 25 + 25 = 50
Therefore the % of married people = (50*100)/(1400/9) = 225/7 = 32.14 (option ‘A’)

NOTE: The same question can also be solved by supposing the number of females also.

QUERY 9

In a class 60% of students pass in Hindi and 45% students pass in Sanskrit. If 25% of them pass both subjects, what percentage of the students fail in both the subjects?

A) 25
B) 35
C) 20
D) 15

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Here the answer should be 100 – [(60+45) – 25] = 20 (option ‘C’)

QUERY 10

In an examination 35% of the candidates failed in Maths and 25% in English while 15 % failed in both subjects. How many candidates passed in one subject but not in the other.

A) 30%
B) 45%
C) 55%
D) 70%

Dinesh Kumar
Failed only in Maths; not in English = 35% – 15%=20%
Failed only in English; not in maths = 25% – 15%=10%
So total of this will be the number of students who passed in one subject but not in other. Here it is 20%+10% = 30% (option ‘A’)

See this diagram also to understand it well:
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