Question 1

Three states X, Y, and Z had students appearing for an exam in 1998 in the ratio 3 : 5 : 6. Next year, the numbers rose by 20%, 10%, and 20% respectively. If in the next year the ratio of students in states X and Z is 1 : 2, determine whether the 19…

Accepted Answer

Introduction / Context: This is a data sufficiency style question disguised as a percentage/ratio problem. We are asked whether the original numbers (1998) can be uniquely determined using the given ratios and percentage changes. Given Data / Assumptions: 1998 ratio X : Y : Z = 3 : 5 : 6 ⇒ numbers = 3k, 5k, 6k. Next year increases: X by 20%, Y by 10%, Z by 20%. Next year X : Z is 1 : 2. Concept / Approach: Compute next-year values as factors of k and check the X : Z ratio. If the ratio condition holds identically (for all k), then k is not determined and original totals cannot be uniquely fixed. Step-by-Step Solution: Next year X = 3k * 1.20 = 3.6kNext year Z = 6k * 1.20 = 7.2kTheir ratio = 3.6k : 7.2k = 1 : 2 (since both sides divide by 3.6k)The ratio holds for any k, so k is not pinned down. Verification / Alternative check: Even if Y’s growth is included, it doesn’t affect the X : Z ratio. Without an absolute count or another independent equation, 1998 totals are undetermined. Why Other Options Are Wrong: Numerical totals (5000, 6000, 75000, 7000) cannot be justified uniquely from the data. Common Pitfalls: Assuming ratios alone can produce exact totals; missing that a free scale factor k remains. Final Answer: Data is insufficient

Question 2

A full tank of petrol in Arun’s motorbike lasts 10 days. If he starts using 25% more petrol per day, for how many days will the same full tank last now?

Accepted Answer

Introduction / Context: This is an inverse-variation question. If daily consumption rises by a certain percentage, the number of days the fixed quantity lasts falls in inverse proportion. Given Data / Assumptions: Original duration = 10 days. New daily use = 25% more ⇒ factor = 1.25 times the old use. Concept / Approach: The total petrol is fixed. Duration (days) * daily use = constant. Hence new days = old days / 1.25. Step-by-Step Solution: New days = 10 / 1.25 = 8 Verification / Alternative check: Let the tank contain 10 units and original daily use be 1 unit/day. After a 25% rise, daily use = 1.25 units/day. Then days = 10 / 1.25 = 8. Why Other Options Are Wrong: 5, 6, and 7 result from over-reducing; 9 assumes too small an increase in daily use. Common Pitfalls: Subtracting 25% from 10 directly (to get 7.5) instead of applying inverse proportion. Final Answer: 8

Question 3

In an exam of 480 students, 85% of the girls and 70% of the boys passed. If the overall pass percentage was 75%, how many boys appeared?

Accepted Answer

Introduction / Context: This problem requires forming an equation from group-wise pass rates and the overall pass rate, then solving for the unknown number of boys. Given Data / Assumptions: Total students = 480. Pass rates: boys 70%, girls 85%. Overall pass % = 75%. Boys = B, girls = 480 − B. Concept / Approach: Total passes = passes by boys + passes by girls. Equate this to 75% of 480 to solve for B. Step-by-Step Solution: 0.70B + 0.85(480 − B) = 0.75 * 4800.70B + 408 − 0.85B = 360−0.15B = −48 ⇒ B = 320 Verification / Alternative check: Boys passed = 0.70 * 320 = 224; girls = 160, girls passed = 0.85 * 160 = 136; total passed = 360 = 75% of 480. Consistent. Why Other Options Are Wrong: 340, 360, 370 lead to totals not equal to 360 passes; 300 also fails the overall percentage. Common Pitfalls: Mixing up which group has which rate, or using 75% of only boys or girls instead of the whole. Final Answer: 320

Question 4

In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was :

Accepted Answer

Total number of votes = 7500 Given that 20% of Percentage votes were invalid => Valid votes = 80% Total valid votes = 7500*(80/100) 1st candidate got 55% of the total valid votes. Hence the 2nd candidate should have got 45% of the total valid votes => Valid votes that 2nd candidate got = total valid votes x (45/100) 7500*(80/100)*(45/100) = 2700

Question 5

Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruits ?

Accepted Answer

The fruit content in both the fresh fruit and dry fruit is the same. Given, fresh fruit has 68% water.so remaining 32% is fruit content. weight of fresh fruits is 100kg Dry fruit has 20% water.so remaining 80% is fruit content.let weight if dry fruit be y kg. Fruit % in freshfruit = Fruit% in dryfruit Therefore, (32/100) x 100 = (80/100 ) x y we get, y = 40 kg.

Question 6

If 20% of a = b, then b% of 20 is the same as :

Accepted Answer

20% of a = b => (20/100) * a = b b% of 20 =(b/100) x 20 = [(20a/100) / 100] x 20= 4a/100 = 4% of a.

Question 7

The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was :

Accepted Answer

Purchase price = R s . 8748 1 - 10 100 3 = Rs. [8748 * (10/9) * (10/9 )* (10/9)] = Rs.12000

Question 8

A student multiplied a number by 3/5 instead of 5/3, What is the percentage error in the calculation ?

Accepted Answer

Let the number be x. Then, ideally he should have multiplied by x by 5/3. Hence Correct result was x * (5/3)= 5x/3. By mistake he multiplied x by 3/5 . Hence the result with error = 3x/5 Then, error = (5x/3 - 3x/5) = 16x/15 Error % = (error/True vaue) * 100 = [(16/15) * x/(5/3) * x] * 100 = 64 %

Question 9

A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are :

Accepted Answer

Given that the student got 125 marks and still he failed by 40 marks => The minimum pass mark = 125 + 40 = 165 Given that minimum pass mark = 33% of the total mark => total mark =33/100 =165 => total mark = 16500/33 = 500

Question 10

if the price of a book is first decreased by 25% and then increased by 20%, then the net change in the price will be :

Accepted Answer

Let the original price be Rs. 100. New final price = 120 % of (75 % of Rs. 100) = Rs. [(120/100) * (75/100) * 100] = Rs. 90. Decrease = 10%

Question 11

A man spends 35% of his income on food, 25% on children's education and 80% of the remaining on house rent. What percent of his income he is left with ?

Accepted Answer

Let the total income be x. Then, income left = (100 - 80)% of [100 - (35 + 25)] % of x = 20% of 40% of x = [(20/100) * (40/100) * 100] % of x = 8 % of x.

Question 12

Gaurav spends 30% of his monthly income on food articles, 40% of the remaining on conveyance and clothes and saves 50% of the remaining. If his monthly salary is Rs. 18,400, how much money does he save every month ?

Accepted Answer

Saving = 50% of (100 - 40)% of (100 - 30)% of Rs. 18,400 = Rs. (50/100 * 60/100 * 70/100 * 18400) = Rs. 3864.

Question 13

In an election only two candidates contested 20% of the voters did not vote and 120 votes were declared as invalid. The winner got 200 votes more than his opponent thus he secured 41% votes of the total voters on the voter list. Percentage votes of …

Accepted Answer

Let there be x voters and k votes goes to loser then 0.8x - 120 = k + (k + 200) k+200 = 0.41x => k = 1440 and (k + 200) =1640 Therefore 1440/3200 x 100 = 45%

Question 14

405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child recieve ?

Accepted Answer

Let the total number of children be x. Then, x * (20% of x) = 405 => x * 20x/100 = 405 1 5 x 2 = 405 => x=45 Number of sweets received by each child = 20% of 45 = 9.

Question 15

If 75% of a number is added to 75, then the result is the number itself. The number is :

Accepted Answer

Let the number be x, Then 75% of x + 75 = x => x - 75x/100 =75 => x = 300 .

Question 16

If A's height is 40% less than that of B, how much percent B's height is more than that of A?

Accepted Answer

Excess of B's height over A's = [(40/(100 - 40)] x 100% = 66.66%

Question 17

A salesman gets commission on total sales at 9%. If the sale is exceeded Rs.10,000 he gets an additional commission as bonus of 3% on the excess of sales over Rs.10,000. If he gets total commission of Rs.1380, then the bonus he received is:

Accepted Answer

Commission up to 10000 = 10000 x 9 100 = 900 Again after 10000, Commission : Bonus 9 : 3 3x : x Therefore, Bonus = 1380 - 900 × 1 4 = R s . 120

Question 18

What percent of 7.2 kg is 18 gms ?

Accepted Answer

Required percentage = (18/7200 * 100)% = 1/4% = 0.25%

Question 19

A's salary is 40% of B's salary which is 25% of C's salary. What percentage of C's salary is A's salary ?

Accepted Answer

A's Salary = 40% of B = 40% of (25% of C) = 40/100[(52/100)*100] % of C = 10% of C.

Question 20

The ratio 5 : 4 expressed as a percent equals :

Accepted Answer

5 : 4 = 5/4 = ( (5/4) x 100 )% = 125%.

Percentage Questions