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Test: Simple & Compound Interest (February 26) - CAT MCQ


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10 Questions MCQ Test Daily Test for CAT Preparation - Test: Simple & Compound Interest (February 26)

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Test: Simple & Compound Interest (February 26) - Question 1
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Mr. Bajaj borrowed Rs. 25,000 from bank at the rate of 12% simple interest. He gave Rs. 10,000 to Ambani at 10% simple interest and Rs. 15,000 to Mittal at 15% simple interest. After 1 year, how much profit (in Rs.) will Bajaj get?

Detailed Solution for Test: Simple & Compound Interest (February 26) - Question 1

Simple interest = 
Profit earned by Mr. Bajaj = SI received by Mr. Bajaj from Ambani + SI received by Mr. Bajaj from Mittal - SI paid by Mr.Bajaj to the bank
= 1,000 + 2,250 - 3,000
= Rs. 250

Test: Simple & Compound Interest (February 26) - Question 2
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Find the rate percent of the simple interest per annum if the sum borrowed becomes double in 5 years.

Detailed Solution for Test: Simple & Compound Interest (February 26) - Question 2

Let the principal amount be 'P' and rate be r.
Amount after 5 years = 2P
Simple interest = A - P = 2P - P = P
According to the question,
P = 
r = 20%
Rate = 20%

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Test: Simple & Compound Interest (February 26) - Question 3
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A man invests Rs. 10,000 for a year, out of which Rs. 4000 are invested at the rate of 5%, Rs. 3500 at the rate of 4% and the remaining at the rate of x%. If at the end of the year, he gets Rs. 500 as interest, then find the value of x.

Detailed Solution for Test: Simple & Compound Interest (February 26) - Question 3

The problem can be solved by using the formula for simple interest:

We need to put the value of each principle amount at a different rate of interest as each of them is invested for a year:
SI = Rs. 500
So, 
⇒ 50,000 = 20,000 + 14,000 + 2500x
⇒ 16,000 = 2500x
⇒ 
⇒ x = 6.4
This is correct answer. 

Test: Simple & Compound Interest (February 26) - Question 4
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A sum of Rs. 4000 was lent partly at 6% and partly at 8% simple interest. If the interest received after one year is Rs. 272, find the ratio in which the money was lent, respectively.
Detailed Solution for Test: Simple & Compound Interest (February 26) - Question 4

Suppose, Rs. x be lent at 6% and Rs. (4000 – x) at 8%.
Then,

6x + 32000 – 8x = 27200
2x = 32000 – 27200 = 4800
x = Rs. 2400
Thus, the two parts are Rs. 2400 and Rs. 1600.
So, required ratio = = 3 : 2

Test: Simple & Compound Interest (February 26) - Question 5
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If the difference between compound interest and simple interest on a certain amount for two years is Rs. 7.35 and the rate of interest is 7%, then find the principal.
Detailed Solution for Test: Simple & Compound Interest (February 26) - Question 5

Let P be the principal.
Compound interest for 2 years = P 
Simple interest for 2 years =

Principle amount = Rs. 1500

Test: Simple & Compound Interest (February 26) - Question 6
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In order to buy a car, a man borrowed Rs. 1,80,000 on the condition that he pay 7.5% interest every year. He would also pay the principal in equal annual installments spread over 21 years. After a certain number of years, the rate of interest reduced to 7%. It is also known that by the end of the agreed period, he will have paid in all Rs. 2,70,900 as interest. For how many years did he pay at the lesser interest rate?
Detailed Solution for Test: Simple & Compound Interest (February 26) - Question 6

Let for x years he paid at 7.5%.

⇒ (13,500x - 12,600x) + 2,64,600 = 2,70,900
⇒ 900x = 2,70,900 - 2,64,600
⇒ 900x = 6300

Test: Simple & Compound Interest (February 26) - Question 7
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Interest obtained on a sum of ₹ 5000 for 3 years is ₹ 1500. Find the rate percent.
Detailed Solution for Test: Simple & Compound Interest (February 26) - Question 7

The interest earned per year would be 1500/3=500. This represents a 10% rate of interest.

Test: Simple & Compound Interest (February 26) - Question 8
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₹ 1694 is repaid after two years at compound interest. Which of the following is the value of the principal and the rate?
Detailed Solution for Test: Simple & Compound Interest (February 26) - Question 8

Let's consider the principal is Rs1400 and rate of interest is 10%.

then after 1st year the interest will be( Rs 1400 × 10% )= Rs140

After completing first year the principal amount will be :-

Principal + rate of interest = Rs ( 1400 + 140) =Rs 1540

In second the principal will be = Rs1540

Rate of interest will be same = 10%

Now after second year the interest will be :-

  1540 x 10% = Rs154

∴ After second year total repaid amount will be:-

=Principal of second year + interest after second year .

=Rs( 1540 + 154) =Rs 1694

Hence option d) matches with the question,

Ans :- Only option (d) matches with the question. there option (d) will be the correct answer.

Test: Simple & Compound Interest (February 26) - Question 9
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Find the rate of interest if the amount after 2 years of simple interest on a capital of ₹ 1200 is ₹ 1440.
Detailed Solution for Test: Simple & Compound Interest (February 26) - Question 9

Interest in 2 years = ₹ 240.
Interest per year = ₹ 120
Rate of interest = 10%

Test: Simple & Compound Interest (February 26) - Question 10
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What is the difference between the simple interest on a principal of ₹ 500 being calculated at 5% per annum for 3 years and 4% per annum for 4 years?
Detailed Solution for Test: Simple & Compound Interest (February 26) - Question 10

5% for 3 years (SI) = 15% of the amount; At the same time 4% SI for 4 years means 16% of the amount. The difference between the two is 1% of the amount. 1% of 500 = ₹ 5

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