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Test: Arun Sharma Based Level 1: Percentages - CAT MCQ


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15 Questions MCQ Test CAT Mock Test Series and 500+ Practice Tests 2024 - Test: Arun Sharma Based Level 1: Percentages

Test: Arun Sharma Based Level 1: Percentages for CAT 2024 is part of CAT Mock Test Series and 500+ Practice Tests 2024 preparation. The Test: Arun Sharma Based Level 1: Percentages questions and answers have been prepared according to the CAT exam syllabus.The Test: Arun Sharma Based Level 1: Percentages MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Arun Sharma Based Level 1: Percentages below.
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Test: Arun Sharma Based Level 1: Percentages - Question 1
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What fraction is equal to 57.12% (approximately)?

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Test: Arun Sharma Based Level 1: Percentages - Question 2
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a% of a + b% of b = 2% of ab, then what percentage of a is b?

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Test: Arun Sharma Based Level 1: Percentages - Question 3
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The height of a triangle is increased by 30%. What can be the maximum percentage increase in length of the base, so that the increase in area is restricted to a maximum of 90%?

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Test: Arun Sharma Based Level 1: Percentages - Question 4
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The length of rectangle is increased by 30% and the breadth is decreased by 25%. What is the percentage change in the area of the rectangle due to this?
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Test: Arun Sharma Based Level 1: Percentages - Question 5
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At an election, the candidate who got 60% of the votes cast won by 200 votes. Find the total number of voters on the voting list, if 66.67% people cast their vote and there were no invalid votes.
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Test: Arun Sharma Based Level 1: Percentages - Question 6
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A man spends 25% of his money on food. After spending 50% of the remaining, he is left with Rs 375. How much money was with that man initially?
Detailed Solution for Test: Arun Sharma Based Level 1: Percentages - Question 6

Assume that he had initially Rs 100.

After spending on food, money left = Rs 75

After spending 50% of Rs 75, he had Rs 37.5

 

Test: Arun Sharma Based Level 1: Percentages - Question 7
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After spending 20% on clothes, 10% on books, 9% on purchasing gift for girl friend and 7% on others, Chandra has a balance of Rs 2,700. How much money was there with him initially?
Detailed Solution for Test: Arun Sharma Based Level 1: Percentages - Question 7

Let initial Amount = Rs. 100

Money left = 100 – (20 + 10 + 9 + 7)

= Rs. (100 – 46)

= Rs. 54

This 54r = 2700

r = 50

100r = 5000

Test: Arun Sharma Based Level 1: Percentages - Question 8
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In a mixture of 100 litres of milk and water, 25% of the mixture is milk. How much water should be added to the mixture, so that milk becomes 20% of the mixture?
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Test: Arun Sharma Based Level 1: Percentages - Question 9
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An amount is lent at y% p.a. simple interest for two years. Instead, had it been lent at 2y% p.a. simple interest for y more years, then the interest would have been five times the earlier interest. Find the value of y.
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Test: Arun Sharma Based Level 1: Percentages - Question 10
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Find the least number of integral years in which a sum of money invested at 20% compound interest per annum will become more than double itself.
Detailed Solution for Test: Arun Sharma Based Level 1: Percentages - Question 10

Given Data:

Compound Interest Rate (r): 20% or 0.20

The sum of money is more than doubled.

Concept:

The formula for compound interest is A = P(1+r/n)(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, t is the time the money is invested for in years. When compounded annually (n=1), this simplifies to A = P(1+r)t.

Solution:

We know that the formula for compound interest, when compounded annually, is A = P(1 + r)^t. Here, we want to find the smallest whole number for time t so that A > 2P.

Substituting A as 2P and r as 0.20 into the formula, we get, ⇒ 2 = (1 + 0.20)t ⇒ 2 = 1.20t

We can now try different values for t until we reach a number where 1.20t > 2.

Using t = 1, we get 1.201 = 1.20 which is not greater than 2.

Using t = 2, 1.202 = 1.44 which is not greater than 2.

Using t = 3, 1.203 = 1.728 which is not greater than 2.

Using t = 4, 1.204 = 2.0736 which is greater than 2.

Therefore, the least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is 4 years.

Test: Arun Sharma Based Level 1: Percentages - Question 11
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Shyam invests ₹₹40000 in some shares in the ratio 1:4:5 which pay dividends of 10%, 15% and 25% (on his investment) for that year respectively. Find his dividend income.
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Test: Arun Sharma Based Level 1: Percentages - Question 12
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The salary of Ajay is 10% more than that of Vivek. Find by what percentage is the salary of Vivek less than that of Ajay?
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Test: Arun Sharma Based Level 1: Percentages - Question 13
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A, B and C donate 8%, 7% and 9%, of their salaries, respectively to a charitable trust. The salaries of A and B are same and the difference between their donations is 259. The total donation of A and B is 1185 more than that of C. The total donation of A and C is what percentage of the total salaries of A, B and C?
Detailed Solution for Test: Arun Sharma Based Level 1: Percentages - Question 13

Let salaries of A and B be Rs. x and salary of C be Rs. y, then

8x/100 – 7x/100 = 259

⇒ x/100 = 259

⇒ x = 25900

Salaries of A and B is Rs. 25900.

Donation of A and B = 25900 × (8 + 7)/100 = 25900 × 15/100 = 3885

Donation of C = 3885 – 1185 = 2700

y × (9/100) = 2700

⇒ y = 30,000

Sum of salaries of A, B and C = 25900 + 25900 + 30000 = 81800

Donation of A = 259 × (8/100) = 2072

Total donation of A and C = 2072 + 2700 = 4772

Percentage of total donation of total salaries of A, B and C = (4772/81800) × 100 = 5.8%

Short Trick:

Let salaries of A, B be 100%

⇒ 8% – 7% = 259

⇒ 1% = 259

⇒ 8% = 2072

⇒ 15% = 3885

⇒ 100% = 25900

Donation of C = 3885 – 1185 = 2700

⇒ 9% = 2700

⇒ 100% = 30,000

Total donation of A and C = 2072 + 2700 = 4772

Total salaries of A, B and C = 25900 + 25900 + 30000 = 81800

∴ Required percentage = 4772/81800 × 100 = 5.8%

Test: Arun Sharma Based Level 1: Percentages - Question 14
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In solution of sugar and water the ratio of sugar and water by weight is 1:4. This solution is heated and in the process it loses 50% weight. What is the ratio of weight of sugar and water in the final mixture?
Detailed Solution for Test: Arun Sharma Based Level 1: Percentages - Question 14

Weight of solution = (1+4) = 5 units weight of sugar = 1 unit weight of water after heating =1.5 units Required ration =1 : 1.5 = 2 : 3

Test: Arun Sharma Based Level 1: Percentages - Question 15
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Dataman Infosys Systems is a Lucknow-based software company which is growing tremendously. It doubled its turnover in 1998 from Rs 50 crores in 1997. Then it tripled its turnover in 1999 and grew by 50% in 2000. What is the turnover at the end of 2000?
Detailed Solution for Test: Arun Sharma Based Level 1: Percentages - Question 15

Turnover in 1998 = Rs 100 cr Turnover in 1999 = Rs 300 cr Turnover in 2000 = Rs 450 cr

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