Percentages
Question 1 
John earns 33.33% more than Peter. By what percentage is Peter's earning less than that of John's?
22 %
 
25 %
 
26 %
 
23 %

Discuss it
Question 1 Explanation:
Let John's income be j and Peter's income be p. Then,
j = p + p × 33.33% = p + p × 100⁄3 % = p + p × 1/3 = 4p/3
⇒ p = 3j/4 = (4  1)j/4 = j  j/4 = j  j × 1/4 = j  j × 100⁄4 % = j  j × 25%.
Therefore, Peter's earning is less than John's earning by 25%.
Question 2 
Mary's salary is reduced by 10%. By what percentage must her new salary be increased in order to gain her old salary?
137⁄9 %  
194⁄9 %  
100/9 %
 
110⁄9 %

Discuss it
Question 2 Explanation:
Let her old salary be Rs 100. Then, her new salary = 100  10 = Rs 90.
So, to gain her old salary, her new salary must be increased by Rs 10. Therefore, the required percentage = (10⁄90) × 100% = 100/9 %.
Question 3 
The price of sugar is decreased by 10%. As a consequence, monthly sales is increased by 30%. Find out the percentage increase in monthly revenue.
17 %  
19 %  
18 %  
None of these 
Discuss it
Question 3 Explanation:
Let the price of sugar be Rs 100 and monthly sales be 100 units. Then,
total revenue = 100 × 100 = Rs 10000.
And, new revenue = 90 × 130 = Rs 11700.
Increase in revenue = 11700  10000 = Rs 1700.
Hence, percentage increase in revenue = (1700/10000) × 100% = 17%.
Question 4 
Jack consumes 75% of his salary. Later his salary is increased by 20% and he increases his expenditures by 10%. Find the percentage increase in his savings.
51%  
60%  
50%  
55% 
Discuss it
Question 4 Explanation:
Let Jack's original salary be Rs 100. Then,
his expenditure = Rs 75,
his savings = Rs 25.
Now, his new salary = Rs 120. So,
new expenditure = (110/100) × 75 = Rs 165/2,
new savings = 120  165/2 = Rs 75/2.
Increase in savings = 75/2  25 = Rs 25/2.
Therefore, percentage increase in savings = (25/2)/25 × 100% = 50%.
Question 5 
Mary buys an item at Rs 25 in a sale and saves Rs 5. Find out the percentage of her savings.
40/3 %  
55/3 %  
50/3 %  
None of these 
Discuss it
Question 5 Explanation:
Original Price of the item = 25 + 5 = Rs 30.
Hence, the required percentage = (5/30) × 100% = 50/3 %.
Question 6 
Barack spends Rs 6650 to buy some goods and gets a rebate of 6% on it. After this, he pays a sales tax of 10%. What is his total expenditure?
Rs 6870.10  
Rs 6876.10  
Rs 6865.10  
Rs 6776.10

Discuss it
Question 6 Explanation:
Rebate received by Barack = 6% of Rs 6650 = 6/100 × 6650 = 3/5 × 665 = Rs 399.
Sales Tax paid by Barack = 10% of Rs (6650399) = 10% of Rs 6251 = Rs 625.10.
Therefore, Barack's total expenditure = Rs (6251 + 625.10) = Rs 6876.10.
Question 7 
Felix spends 66.66% of his salary and saves Rs 1200 every month. Calculate his monthly expenditure in Rupees.
Rs 2402  
Rs 2400  
Rs 2401  
Rs 2405 
Discuss it
Question 7 Explanation:
Let Felix's monthly salary be Rs x. Then,
(100  66.66)% of x = Rs 1200
⇒ 33.33 % of x = Rs 1200
⇒ x/3 = Rs 1200
⇒ x = Rs 3600.
Therefore, his monthly expenditure = 3600  1200 = Rs 2400.
Question 8 
Jack and Robert appeared in an examination. Robert scored 9 marks less than Jack. Jack's score was 56% of the sum of their scores added together. Calculate their individual scores.
22 and 33  
41 and 35  
40 and 35  
42 and 33 
Discuss it
Question 8 Explanation:
Let Robert's score be x. Then, Jack's score = x+9.
Now, x+9 = 56% of [(x+9) + x]
⇒ x+9 = 14/25 × (2x + 9)
⇒ 25 × (x+9) = 14 × (2x+9)
⇒ 25x + 225 = 28x + 126
⇒ 3x = 99 ⇒ x = 33.
Therefore, Robert scored 33 marks and Jack scored 42 marks.
Question 9 
Ram spends 20% of is salary on food, 15 % of remaining on cloths, and 400 on entertainment. If his salary is 10000, how much he spends on food?
2000  
3000  
1500  
2500 
Discuss it
Question 9 Explanation:
10000*20/100 = 2000
Question 10 
Ram spends 20% of is salary on food, 15 % of remaining on cloths, and 400 on entertainment. If his salary is 10000, how much he spends on cloths?
1100  
1200  
1500  
1000 
Discuss it
Question 10 Explanation:
[10000(10000*20/100)]*15/100 = 1200
Question 11 
Ram spends 20% of is salary on food, 15 % of remaining on cloths, and 400 on entertainment. If his salary is 10000, how much salary he saves at the end of month?
1400  
3600  
6400  
2000 
Discuss it
Question 11 Explanation:
Total expenditure = [10000*20/100] + [[10000(10000*20/100)]*15/100] +400
= 2000+1200+ 400 = 3600
Savings = 100003600 = 6400
Question 12 
5 years ago age of Ram was 50 % less than Shyam’s age. If the ratio of Shyam’s present age to Ram’s present age 4:3. What will be Ram’s age after 7.5 years?
25 years  
20 years  
20 years  
15 years 
Discuss it
Question 12 Explanation:
Say Ram’s present age = R,
Shyam’s present age = S,
R:S = 3:4,
R = 3S/4  (1)
5 years ago Ram’s age = R5,
5 years ago Shyam’s age S5, and according to given condition, R5 = (S5)/2  (2)
From 1 and 2:
(R  5) = ((4R/3)5)/2,
6R  30 = 4R  15,
R = 15/2 = 7.5 years,
After 7.5 years, Ram’s age = 7.5 + 7.5 = 15 years.
Question 13 
5 years ago the ratio of Shyam’s age to Ram’s age is 3:2. If Ram’s present age is 25% less than Shyam’s present age. What will be Ram’s age after 10 years?
20 years  
15 years  
25 years  
20 years 
Discuss it
Question 13 Explanation:
Say Ram’s present age = R
Shyam’s present age = S
S = R+S/4(1)
5 years ago:
(S5)/(R5) = 3/2(2)
from 1 and 2:
(8R/3) 10 = (9R/3) – 15
R =15
After 10 years Ram’s age = 25 years
Question 14 
A product is sold at two consecutive discounts of 30% and subsequently 40%. If the product is sold for 1500, what is the marked price on product?
3500  
3600  
3550  
3571 
Discuss it
Question 14 Explanation:
Say MP is the marked price
=> (70.MP/100)*(60/100) =1500
=> 7*0.6 MP = 1500
=> MP = 1500/0.42 = 3571
Question 15 
A product is sold at two consecutive discounts of 30% and subsequently 40%. If the marked price on the product is 1500, What is the selling price of the product?
420  
360  
600  
630 
Discuss it
Question 15 Explanation:
SP = (70*1500/100)*(60/100) = 0.42*1500 = 630
Question 16 
Sudheer’s family can use the water up to 10 days when the tank is full. If the water consumption of his family is increased by 25% per day, how many days will the water tank last?
5  
6  
7  
8 
Discuss it
Question 16 Explanation:
Let the water capacity of the tank be x liters. Then,
Initial water consumption rate = x/10 ltr per day
New water consumption rate after the increase by 25% = x/10 * (1 + 25/100) ltr per day = x/10 * 1.25 = x/8 ltr per day
The water tank last in number of days = full tank capacity in ltr / new water consumption rate in ltr per day = x / (x/8) = 8 days.
There are 16 questions to complete.