QUESTIONS ON PERCENTAGE (PART-II)

QUERY 11

In an examination, 70% students passed in English and 75% in Hindi while 20% failed in both the subjects. If 325 students passed in both the subjects, the total number of students is

A) 400
B) 500
C) 340
D) 460

MAHA GUPTA
Failed in both the subjects are 20%, means the rest 80% includes PASSED IN BOTH, FAILED ONLY IN ENGLISH and FAILED ONLY IN HINDI. Now we have only to know the total of FAILED ONLY IN ENGLISH and FAILED ONLY IN HINDI. To know PASSED IN BOTH. See how:

If total students are 100 then failed in English = 100 – 70 = 30. As 20% failed in both, 20 of them have failed in Hindi also. Therefore FAILED IN ENGLISH ONLY = 30 – 20 = 10 —————-(i)

Failed in Hindi = 100 – 75 = 25
As 20% failed in both, 20 of them have failed in English also. Therefore FAILED IN HINDI ONLY = 25 – 20 = 5 ——————-(ii)

Total of (i) and (ii) = 10 + 5 = 15

So passed in both = 80 – 15 = 65

Now, if passed in both are 65 total number of students = 100
if passed in both are 325 total number of students is (100/65)*325 = 500 (option ‘B’)

 

QUERY 12

A reduction of 20% in the price of sugar enables a purchaser to obtain 3 kg more for 120; the original price of sugar is?

A) Rs 8 per kg
B) Rs 7 per kg
C) Rs 10 per kg
D) Rs 12 per kg

MAHA GUPTA
Reduction in the price = 20%
Therefore the purchaser’s saving on = 20% of 120 = Rs 24
Thus he’ll be able to buy 3 kg of sugar in 24 now
Hence the reduced price of Sugar = 24/3 = Rs 8 per kg

According to 20% reduction in the price
If Rs 80 per kg is the reduced price the original price = 100 per kg
If 8 is the reduced price the original = (100/80)*8 = Rs 10 per kg (option ‘C’)

QUERY 13

After an increase in sugar price by 40%, a family reduced its consumption of sugar to the extent that there should be an increase on sugar expenses only by 10%. If the earlier consumption of sugar was 28 kg, what will be their new consumption?

A) 20 kg
B) 18 kg
C) 22 kg
D) 25 kg

MAHA GUPTA
One should avoid trying to solve questions by assuming ‘x’ etc as far as possible as it’s time-consuming generally.

Now, let the earlier price of sugar = Rs 10 a kg
Then price after the increase = 10*140/100 = 14 a kg

Total monthly expense on sugar before increase = 28*10 = 280
And this after the increase that he wants i.e. 10% = 280*110/100 = 308

But the new price is Rs 14 a kg

So the consumption of sugar at present = 308/14 = 22 kg (option ‘C’)

QUERY 14

If 1/5 of A = 0.25 of B = 30% of C, then A : B : C is equal to?

A) 12 : 15 : 10
B) 8 : 16 : 35
C) 15 : 12 : 10
D) 10 : 15 : 12

MAHA GUPTA
1/5 of A = 0.25 of B = 30%
=> A/5 = B/4 = 3C/10

Taking A/5 = B/4 => A/B = 5/4 => A : B = 5 : 4 —-(i)
Taking B/4 = 3C/10 => B/C = 12/10 => B : C = 6 : 5 —-(ii)

Now multiplying (i) by 3 and (ii) by 2
A : B : C = 15 : 12 : 10 (option ‘C’)

QUERY 15

There is 2.5% annual increase in population of a city but cause of transfer there is annual decrease of population by 0.5%, then find the increase% of population in 2 yrs?

A) 4.4%
B) 4.04%
C) 4%
D) 4.2%

MAHA GUPTA
Net effect of increase and decrease annually = 2.5 – 0.5 = 2% increase
Let the population in the beginning = 100
So population after 1 year = 100 + 2% of 100 = 102
And population at the end of 2 years = 102 + 2% of 102 = 104.04

Hence increase in percentage in 2 years = 4.04 (option ‘B’)

TRICK
Formula
Letting %increase ‘a’
Then net effect in 2 periods = a + a + (a²)/100

Therefore it is = 2 + 2 + (2²)/100 = 4.04 (option ‘B’)

QUERY 16

A man spends 75% of his income. If his income is increased by 20% and he increases his expenditure by 10%, his savings are increased by?

A) 45%
B) 50%
C) 55%
D) 57%

MAHA GUPTA
Let his initial income = 100
Then his expenditure = 75
So, his savings = 100 – 75 = 25

His income after = 100 + 20% of 100 = 120
And expenditure after = 75 + 10% of 75 = 82.50
So his savings now = 120 – 82.50 = 37.50

Therefore increase in his savings = 37.50 – 25 = 12.50

Now increase on 25 = 12.50
Hence increase on 100 = (12.50/25)*100 = 50% (option ‘B’)

QUERY 17

1 liter of water is added to 5 liters of alcohol-water solution containing 40% alcohol strength. The strength of alcohol in the new solution will be?

A) 30%
B) 100/3%
C) 101/3%
D) 33%

MAHA GUPTA
Alcohol in the earlier mixture = 40% of 5 liters = 2 liters
Mixture after addition of 1 liter of water = 5 + 1 = 6 liters

Therefore strength of alcohol in the new mixture in percentage = (2/6)*100 = 100/3 % (option ‘B’)

QUERY 18

In an election between two candidates, 75% of voters cast their votes, out of which 2% of votes declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. The total number of voters enrolled were?

A) 16000
B) 16400
C) 16800
D) 18000

MAHA GUPTA
Let the total number of enrolled voters = 200
Therefore the number who cast votes = 75% of 200 = 150
And invalid votes = 2% of 150 = 3
So valid votes = 150 – 3 = 147

Number of votes got by the candidate = 75% of 147 = (3/4)*147 = 441/4

But the actual votes got by the candidate = 9261

Now, if the votes got is 441/4 the total number of voters enrolled = 200
If the votes got is 9261 the total number of voters enrolled = (200*4*9261)/441 = 16800 (option ‘C’)

QUERY 19

At a discount of 10% of the entire purchase Ram could have bought 1 more kg of sugar by paying only 5% of the original amount more. How many kilograms of sugar has Ram bought?

A) 7 kg
B) 5 kg
C) 6.5 kg
D) 6 kg

MAHA GUPTA
Suppose amount to be paid by Ram before discount = Rs 100
Therefore the amount paid in actual i.e. after discount of 10% = Rs 90

Had he given 5% more of the original amount, the amount that would have been paid = Rs 105; but at this amount he would have got 1 kg more of sugar.

Therefore price of 1 kg of sugar = amount of discount + amount in excess of original amount = 10 + 5 = 15

But in actual he gave Rs 90
So quantity of sugar bought by Ram = 90/15 = 6 kg (option ‘D’)

QUERY 20

In an election 68 votes are invalid. the winning candidate secures 52% and wins by 98 votes. The total number of votes polled are?

A) 6000
B) 4500
C) 3534
D) 2518

MAHA GUPTA
Winning candidate secures 52% of votes (valid votes); means the loosing candidate secures 100 – 52 = 48% of the valid votes.

Means the winning candidate’s winning margin is 52 – 48 = 4%
But the winning margin in terms of number is 98 votes

Therefore we can say that 98 is 4% of the valid votes
Hence the number of valid votes = (100/4)*98 = 2450
So the number of total votes = valid votes + invalid votes = 2450 + 68 = 2518 (option ‘D’)