23-08-2021 Answers

1. If 245% of x is 986 what is (x% of 245) + 90?

Answer: 1076

Solution: x% of y is equal to y% of x.

As 245% of x = 986,

x% of 245 = 986.

Hence (x% of 245) + 90 = 986+90 = 1076

2. After the new CEO took over, the revenue of the company increased by 50% every quarter. If the difference in the revenue between second and third quarter after the CEO took over was 450 millions, what was the third quarter revenue?

Answer: 1350 millions

Solution: Let the revenue at the end of second quarter be x.

Revenue at the end of third quarter is x + x*50/100 = 1.5x

The difference 1.5x - x = 0.5x = 450,

Hence x=900 millions.

Revenue at the end of third quarter = 1.5x = 1.5*900 = 1350 millions.

3. A student multiplies a number by 5 instead of dividing it by 5. What is the percentage change in the resulting value due to this mistake?

Answer: 2400%

Solution: Let the number be n.

Expected result = n/5

Obtained result = 5n

Difference = 5n - n/5 = 24n/5

Percentage change = 100 * (24n/5)/(n/5) = 2400%

4. If x% of x is 64, then x = ?

Answer: 80

Solution: x% of x = 64

So x * x/100 = 64

x2 = 6400

x = 80.

5. If the price of diesel increases by 10% and Babu intends to spend only an additional 5% on petrol, by how much percentage should he reduce the consumption?

Answer: 4.55%

Solution: Let the current price of unit quantity of diesel be x. New price=1.1x.

Let reduced quantity be y.

y*1.1x = 1.05x,

y=21/22

Reduction = 1 - 21/22 =1/22 = 4.545% = 4.55% approx

6. A,B,C are going for a tour. They shared the expense that occurred in the tour equally. A paid for the accommodation (lodging). B spent Rs. 20000 as travel expense. C spent 30% of the overall expense for other items. If after final calculation, C paid Rs. 3300 to A and B paid Rs. 13000 to A, what was the percentage of expense towards accommodation?

Answer: 49.8% approximately.

Solution: As the expense is shared equally, one-third of expense is what B pays = 20000+13000 = Rs.33000.

Hence overall expense = 3*33000 = Rs.99000.

Amount C paid = 33000 - 3300 = 29700.

Hence amount A paid for boarding= 99000 - (amount initially paid by B and C)

= 99000 - (20000 + 29700)

= 49300.

% of accommodation expense = (49300/99000) * 100 = 49.8% approximately

7. Due to a 25% price hike in sugar price, a family is able to purchase 20kg less sugar for Rs.4400. Find the price of the sugar per kg after price hike.

Answer: None of these

Solution: Hike ratio = 25/100 = 1/4.

Hence the ratio of decrease in quantity = q * 1/(4+1) = q/5

q/5 = 20kgs.

Hence q=100kgs.

Initial price = 4400/100 = Rs.44

Price after hike = 44 * 1.25 = Rs.55.

8. A shopkeeper offers a discount of 25% on a TV. Since one of the customers who wanted the TV was a very good friend of the shopkeeper, an additional discount of 12% was offered to the customer on the discounted price. What was the total discount offered on the TV?

Answer: 34%

Solution: Let the marked price be Rs.x.

So final selling price for the costumer = x*75/100*88/100 = x*66/100.

So total discount = 100-66 = 34%.

9. Two numbers are respectively 20% and 50% more than the third number. What percentage of the second number is the first number?

Answer: None of these

Solution: Let the third number be x. First num=1.2x and second num=1.5x.

Required % = 100 * 1.2x/1.5x = 100 * 4/5 = 80%

10. In a village, 20% of the tobacco chewers have oral cancer. 80% of the people having oral cancer are tobacco chewers. If 30% of the village population chew tobacco, what is the percentage of the population having oral cancer?

Answer: 7.5%

Solution: Assume the population of the village is 100.

30% of 100 = 30 people chew tobacco.

20% of 30 tobacco chewers = 6 have oral cancer.

These 6 constitute 80% of the people having oral cancer.

Hence total % of people having oral cancer = 100* (6/80) = 7.5%

11. The price of a book in four different shops and the successive discounts provided are given below. Choose the option in which the price of the book is the least.

 

Shop A) 10%, 5%, 5% discount on a marked price of Rs.175

Shop B) 25% discount on a marked price of Rs.200

Shop C) 12.5%, 12.5% discount on a marked price of Rs.205

Shop D) 10%, 15% discount on a marked price of Rs.190

Answer: Shop A

Solution: Shop A final price = 175 * 0.9 * 0.95 * 0.95 = 142 approx

Shop B final price = 200 * 0.75 = 150

Shop C final price = 205 * 0.875 * 0.875 = 157 approx

Shop D final price = 190 * 0.9 * 0.85 = 145 approx

12. In an examination 70% of the candidates passed in history and 50% in geography and 20% failed in both the subjects. If 500 students passed in both the subjects, then how many candidates appeared for the exam?

Answer: 1250

Solution: Let total number of students be x.

x - 0.2x = Total number of students who passed = 0.7x + 0.5x - 500

Solving x = 500/0.4 = 1250

13. There are two distinct natural numbers. Each is increased by 10 and then by the percentage as each was increased for the first time. Each number finally results in 72. Find the product of the two numbers

Answer: 100

Solution: Let a number be x.

After first hike it is x+10.

First time hike factor= 10/x

 

Hence, (x+10)( 1 + 10/x) = 72,

(x-2)(x-50) = 0,

Hence the numbers are 2 and 50 and their product is 100.

14. In a year after two successive price hike, the petrol price became 15/8 times the price in the beginning of the year. The second hike was double the first hike in terms of percentage. What was the price hike in percentage the first time?

Answer: 25%

Solution: Let x be the price in the beginning of the year and y be the first time hike.

x (1+y) (1+2y) = 15x/8,

(y - 1/4)(y+7/4) = 0.

As the hike is positive y = 1/4 = 0.25

Hike as % = .25*100 = 25%

15. P is six times as large as Q. Find the percent that Q is less than P?

Answer: 83%

Solution: Let us assume Q = X, then P = 6X

Q is less by (6X – X) = 5X

5X/6X * 100 = 83% approx.

16. If a discount of 30% is given on a pen, the selling price is Rs.21. What will be the selling price of the same pen when a discount of 20% is given?

Answer: Rs.24

Solution: Let marked price be Rs.x.

So x*70/100 = 21.

x = 21/0.7 = Rs.30

Hence selling price at discount of 20% = 30*0.8 = Rs. 24

17. By how much Percentage is three fourth of 80 less than two third of 120?

Answer: 25

Solution: Three fourth of 80 = 80 * 3/4 = 60.

Two third of 120 = 120 * 2/3 = 80.

Percentage of less = [(80-60) / 80] * 100 = 25%

18. As the price of salt increased by 20%, 4 kgs of less salt is available for Rs.120. What was the original price of salt per kg?

Answer: Rs.5

Solution: Let initially x kgs of salt be brought for Rs.120.

Original price = 120/x per kg.

 

 

Now due to 20% hike, (x-4) kgs available for Rs.120

Hence 1.2 * 120/x * (x-4) = 120,

Solving x=24.

 

 

Hence original price of salt = 120/24 = Rs.5 per kg

19. In a company, 33.33% of the employees are females. Half of the females are married. One-third of the married females have children. 75% of the males in the company are married and two-third of the married males have children. Assuming no two employees are married to each other and only married can have children, what percentage of the employees do not have children?

Answer: 61.11% approx

Solution: Let the total num of employees be x. Hence num of females = x/3 and num of males = 2x/3.

Num of females not married = x/3 * 1/2 = x/6

Num of females married and not having children = x/3 * 1/2 * 2/3 = x/9

Num of males not married = 2x/3 * 1/4 = x/6

Num of males married and not having children = 2x/3 * 3/4 * 1/3 = x/6

Hence total num of employees not having children = x/6 + x/6 + x/9 + x/6 = 11x/18

Expressing in % it is 61.11% approx

20. The variables f,a,b,c,m,n are related as in the below equation.

f = 2abc + 5mn

If a,b,c,m,n are increased by 25%,60%,-10%,20% and 50% respectively, what is the percentage increase in f?

Answer: 80%

Solution: As per the data given,

f = 2 * 5a/4 * 8b/5 * 9c/10 + 5 * 6m/5 * 3n/2

f = 2abc * 18/10 + 5mn * 18/10

f = (2abc + 5mn) * 1.8

Hence % increase in f = 100 * 0.8/1 = 80%

21. A medical college student has to secure 35% marks in certain exams to pass. He got 123 marks and failed by 17 marks. Find the total marks for which he wrote the exams.

Answer: 400

Solution: Let the total marks be x.

x * 35/100 - 17 = 123,

x=140*100/35, solving x=400.

22. If a:b = 5:3, what percentage of 3a is (3a + 4b)?

Answer: 180%

Solution: Let a = 5x and b = 3x.

So the required percentage is (3a+4b)/3a * 100 = (15x+12x)/15x * 100

=27/15 * 100 = 180%.

23. If 10% of the electricity bill is deducted, Rs.450 is still to be paid. What was the bill amount?

Answer: Rs.500

Solution: Let the electricity bill be Rs.x.

So x*0.9 = 450

x = 450/0.9 = 500.

24. What is the net discount on two successive discounts of 24% and 10% ?

Answer: 31.6 %

Solution:Let the marked price be Rs.x.

So final selling price for the costumer = x*76/100*90/100 = x*68.4/100.

So total discount = 100-68.4 = 31.6 %.

25. The carrot price after two successive price hike of 10% and 20% is Rs.33 per kilogram. What was the price of carrot per kilogram before these hikes?

Answer: Rs.25

Solution: Let initial price per kg be x.

% Hike = (a + b + ab/100) = (10+20+ 10*20/100) = 32%.

Hence price after hike = 1.32x which is 33.

Hence original price = 33/1.32 = Rs.25 per kg