# Percentages, Fractions, Ratio

Percentages and fractions are core topics from which you should expect questions in most MBA entrance tests such as the XAT and TANCET. Concepts usually tested include converting fractions to percentages, percentages to fractions, equating a parameter given as a percentage and as a number and percentage increase and percentage decrease. Quite often these questions are framed as word problems. Usually one to two questions appear testing this basic concept.

If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?

- 10%
- 12%
- 8%
- 6.67%
- 12.5%

**Choice (3)**8% Correct answer- Explanatory answer
- % change in price
- Easy

A shepherd has 1 million sheeps at the beginning of Year 2000. The numbers grow by x% (x > 0) during the year. A famine hits his village in the next year and many of his sheeps die. The sheep population decreases by y% during 2001 and at the beginning of 2002 the shepherd finds that he is left with 1 million sheeps. Which of the following is correct?

- x > y
- y > x
- x = y
- Cannot be determined

**Choice (1)**x > y Correct answer- Explanatory answer
- % increase and decrease
- Medium

In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes and there are no invalid votes, by how many votes did it lose the election?

- 300,000
- 168,000
- 36,000
- 24,000

**Choice (3)**36,000 Correct answer- Explanatory answer
- % more than
- Medium

A candidate who gets 20% marks fails by 10 marks but another candidate who gets 42% marks gets 12% more than the passing marks. Find the maximum marks.

- 50
- 100
- 150
- 200

**Choice (2)**100 Correct answer- Explanatory answer
- Comparing % difference
- Easy

When processing flower nectar into honeybees' extract, a considerable amount of water gets reduced. How much flower nectar must be processed to yield 1kg of honey, if nectar contains 50% water, and the honey obtained from this nectar contains 15% water?

- 1.5 kgs
- 1.7 kgs
- 3.33 kgs
- None of these

**Choice (2)**1.7 kgs Correct answer- Explanatory answer
- Mixtures and alligation
- Medium

A vendor sells 60 percent of apples he had and throws away 15 percent of the remainder. Next day he sells 50 percent of the remainder and throws away the rest. What percent of his apples does the vendor throw?

- 17
- 23
- 77
- None of these

**Choice (2)**23 Correct answer- Explanatory answer
- % of % of a quantity
- Easy

If the cost price of 20 articles is equal to the selling price of 16 articles, what is the percentage of profit or loss that the merchant makes?

- 20% Profit
- 25% Loss
- 25% Profit
- 33.33% Loss

**Choice (3)**25% Profit Correct answer- Explanatory answer
- % profit, % loss
- Easy

30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years?

- 15%
- 20%
- 80%
- 70%

**Choice (3)**80% of football players are less than or equal to 50 years Correct answer- Explanatory answer
- Classification and percentage
- Hard

If the price of petrol increases by 25%, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?

- 25%
- 16.67%
- 20%
- 33.33%

**Choice (3)**Cut down consumption of petrol by 20% Correct answer- Explanatory answer
- % increase in price
- Easy

Peter got 30% of the maximum marks in an examination and failed by 10 marks. However, Paul who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What was the passing marks in the examination?

- 35
- 250
- 75
- 85

**Choice (4)**Pass mark is 85. Total marks is 250. Correct answer- Explanatory answer
- Pass mark and total marks
- Easy

40% of 70 is x% more than 30% of 80. Find x.

- 33.33%
- 40%
- 16.67%
- 25%
- 14.28%

**Choice (3)**16.67% more than 30% of 80. Correct answer- Explanatory answer
- % of % of a quantity
- Easy

John weighs twice as much as Maria. Maria's weight is 60% of Bob's weight. Dave's weight is 50% of Lee's. Lee weighs 190% as much as John does. Which of these 5 persons weighs the least?

- Bob
- Dave
- John
- Lee
- Maria

**Choice (5)**Maria weighs the least. Correct answer- Explanatory answer
- Comparing weights
- Medium
- TANCET 2008

Tina, Mina, Gina, Lina and Bina are 5 sisters, aged in that order, with Tina being the eldest. Each of them had to carry a bucket of water from a well to their house. Their buckets' capacities were proportional to their ages. While returning, equal amount of water got splashed out of their buckets. Who lost maximum amount of water as a percentage of the bucket capacity?

- Tina
- Mina
- Gina
- Lina
- Bina

**Choice (5)**Bina Correct answer- Explanatory answer
- Comparing % of water lost
- Easy
- XAT 2012

Joan started work 2 years ago. Her starting salary was half of Mike's salary at that time. Each year since then Joan and Mike have received a rise of 10% in their respective salary. What percentage (to the nearest percent) of Mike's current salary is Joan's current salary?

- 45
- 46
- 48
- 50
- 220

**Choice (4)**50 Correct answer- Explanatory answer
- Percentage increase
- Easy
- TANCET 2008

If S is 150 percent of T, then T is what percent of S + T?

- 33.33%
- 40%
- 75%
- 80%
- 85%

**Choice (2)**40% Correct answer- Explanatory answer
- T as a % of (S + T)
- Easy
- TANCET 2012

The taxes for various income slabs are given below:

Income Slab (I) Tax rate I ≤ 500 0 500 < I ≤ 2000 5% 2000 < I ≤ 5000 10% 5000 < I < 10,000 15% There are 15 persons working in an organization. Out of them 3 to 5 persons are falling in each of the income slabs mentioned above. Which of the following is the correct tax range of the 15 person? (e.g., If one is earning Rs. 2000, the tax should be : 500 * 0 + 1500 * 0.05)

- 1350 to 7350, both excluded
- 1350 to 9800, both included
- 2175 to 7350, both excluded
- 2175 to 9800, both included
- None of the above

**Choice (A)**1350 to 7350, both excluded Correct answer- Explanatory answer
- Range of taxes
- Hard
- XAT 2015

## XAT TANCET Practice Questions - Listed Topic wise

- Number Theory
- Permutation Combination
- Probability
- Inequalities
- Geometry
- Coordinate Geometry
- Mensuration
- Trigonometry
- Data Sufficiency
- Percentages
- Profit Loss
- Ratio Proportion
- Mixtures & Alligation
- Speed Distance & Time
- Pipes, Cisterns & Work, Time
- Simple & Compound Interest
- Races
- Averages & Statistics
- Progressions : AP, GP & HP
- Set Theory
- Clocks Calendars
- Linear & Quadratic Equations
- Functions
- English Grammar
- General Awareness