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Test Level 2: Simple & Compound Interest - 2 - CAT MCQ


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20 Questions MCQ Test Level-wise Tests for CAT - Test Level 2: Simple & Compound Interest - 2

Test Level 2: Simple & Compound Interest - 2 for CAT 2024 is part of Level-wise Tests for CAT preparation. The Test Level 2: Simple & Compound Interest - 2 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 2: Simple & Compound Interest - 2 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 2: Simple & Compound Interest - 2 below.
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Test Level 2: Simple & Compound Interest - 2 - Question 1

Mr. Magnet got a loan of Rs. 21,000 at 10% simple interest. He repaid that loan in 24 equal monthly installments, each being paid at the end of every month starting from the next year; that means for the first year, he did not pay anything and for the next 2 years he paid the installments and cleared the loan exactly by the end of the third year. What was approximate each installment he paid?

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 1

Let equal installment = Rs. x

21,000 × 1.3 = 26.3x
⇒ x ≈ 1,038

Test Level 2: Simple & Compound Interest - 2 - Question 2

Find the simple interest on Rs. 2000 at 6% per annum for a period of 1 year and 7 months.

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 2

Time (T) = 1 year 7 months =
Simple Interest = 

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Test Level 2: Simple & Compound Interest - 2 - Question 3

A sum of money at compound interest doubles in 1 year. In how many years will it amount to 8 times of itself?

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 3

A = P

Now, 8P = P
⇒ 8P = P (2)t
Or, 23 = 2t
∴ t = 3
Required time = 3 years

Test Level 2: Simple & Compound Interest - 2 - Question 4

Sachin borrowed Rs. 28,000 from Yuvraj at 12% simple interest. After 1 year, he paid the interest and Rs. 10,000 extra. After 6 months more, if Sachin wants to clear the debt, then how much money does he have to pay Yuvraj?

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 4

 

Test Level 2: Simple & Compound Interest - 2 - Question 5

Ritesh deposited Rs. 8000 in State Bank of India. He had to pay 10% of the interest of the first year as his college fees, after which Rs. 900 of the interest amount was left. Find the rate percentage at which the interest was paid.

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 5

Let the rate % be x.

10% of interest paid
⇒ 90% of interest left = Rs. 900
So, complete interest (100%) = Rs. 1000

= 12.5%

Test Level 2: Simple & Compound Interest - 2 - Question 6

X invested a sum at compound interest payable half-yearly. If the compound interest in November 2003 was Rs. 225 and in May 2004, it was Rs. 236.25, find the annual rate of interest.

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 6

Difference in C.I. of two successive periods = S.I. on C.I. of the earlier period
11.25 is S.I. on Rs. 225 at the same rate for six months.

⇒ r = 5%
Annual rate of interest = 10%

Test Level 2: Simple & Compound Interest - 2 - Question 7

Divide Rs. 6000 into two parts so that the simple interest on the first part for 2 years at 6% p.a. may be equal to the simple interest on the second part for 3 years at 8% p.a. (in Rs.).

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 7

Let the two parts be P1 and P2.
According to the question,

⇒ P1 : P2 = 2 : 1
∴ P1 = 6000 × 2/3 = 4000 and P2 = 2000

Test Level 2: Simple & Compound Interest - 2 - Question 8

Amit invested two equal sums of Rs. 5,000 for 2 years at 10% C.I, one at C.I. payable yearly and the other at C.I. payable half yearly. Find the approximate difference in amounts that he will get at the end of 2 years.

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 8

Principal = Rs 5000
Rates = 10% for yearly and 5% for half yearly
Times = 4 periods for compounded half yearly and 2 periods for compounded yearly
Difference = 5,000 = 5,000 (1.215 – 1.210) = Rs. 28

Test Level 2: Simple & Compound Interest - 2 - Question 9

Dhiraj invests a part of Rs. 8000 at 4% p.a. and the remainder at 5% per year. His annual income from the investments is Rs. 350. What amounts of money (in rupees) has he invested at each rate, respectively?

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 9

Let the amount invested at 4% be x and that at 5% be (8000 - x).

⇒ 4x + 40,000 - 5x = 35,000
Therefore, x = 5,000
Hence, amounts invested by Dhiraj at 4% and 5% are Rs. 5,000 and Rs. 3,000 respectively.

Test Level 2: Simple & Compound Interest - 2 - Question 10

A sum was put on simple interest at a certain rate for 4 years. Had it been put at a 5% higher rate, it would have fetched Rs. 200 more. Find the sum.

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 10

Let the sum be P, Rate of interest be r.
So, according to the question:
P × r × 4 + 200 = P × (r + 0.05) × 4
4Pr + 200 = 4Pr + 0.2P
200 = 0.2P
P = Rs. 1000

Test Level 2: Simple & Compound Interest - 2 - Question 11

At a certain rate of simple interest, Rs. 700 in 2 years amounts to Rs. 840. If the rate of interest is increased by 2%, what will be the amount after 3 years?

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 11

SI = 
840 - 700 = 700 × 2 × 
140 = 14R
R = 10% per year
Then, total amount after 3 years = 700 + 700 × (10 + 2) × 3/10
Total amount after 3 year at a rate of (10 + 2)% per year = 700 + 252 = Rs. 952

Test Level 2: Simple & Compound Interest - 2 - Question 12

A man borrowed Rs. 12,000 at 5% simple interest, Rs. 15,000 at 8% simple interest and Rs. 20,000 at 12% simple interest. He lent all this money to another person at the rate of 10% compounded annually. How much money will the man gain after 2 years?

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 12

Amount he has to pay after 2 years

= 13,200 + 17,400 + 24,800 = Rs. 55,400
He lent Rs. 12,000 + Rs. 15,000 + Rs. 20,000 at 10% compound interest.
So, after 2 years, he will get back 47,000=Rs. 56,870
So, money gained = Rs. 1470

Test Level 2: Simple & Compound Interest - 2 - Question 13

A money lender took a loan from bank at 22% simple interest and he lent all this money to another person at a rate of 5k% simple interest, where k depends on the principal P such that (k - 1) × 104 ≤ P < k × 104. What is the minimum amount of loan that he must take so that he does not incur any loss?

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 13

There should be no loss if
22% ≤ 5k%
k ≥ 22/5
k ≥ 4.4
For minimum amount, k = 4.4
So,
(k - 1) × 104 ≤ P
(4.4 - 1) × 104 ≤ P
34000 ≤ P
Therefore, minimum amount of loan is Rs. 34,000

Test Level 2: Simple & Compound Interest - 2 - Question 14

Shweta borrowed some money under simple interest. If she pays Rs. 10,000 at the end of 1 year and Rs. 18,200 at the end of second year, the debt will be cleared. Even if she pays Rs. 15,000 at the end of 1 year and Rs. 12,800 at the end of second year, then also the debt will be cleared. What is the rate of interest?

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 14

As in the first case, she is paying Rs. 10,000 + Rs. 18,200 = Rs. 28,200
As in the second case, she is paying Rs. 15,000 + Rs. 12,800 = Rs. 27,800
So, the difference of Rs. 400 (Rs. 28,200 - Rs. 27,800) is nothing but the interest of Rs. 5,000 (Rs. 15,000 - Rs. 10,000) for 1 year.

⇒ r = 8%

Test Level 2: Simple & Compound Interest - 2 - Question 15

A man borrows a sum of money at simple interest at the rate of 5% per annum and lends it out at 4% per annum compound interest, payable yearly. Find his net gain or loss at the end of 2 years as a percentage of sum borrowed by him.

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 15

SI (to be paid) = = 0.1P
CI (to be received) = A - P = P - P = 0.0816P
So, he has to pay 0.1P and he gets 0.0816P.
So, loss = 0.1P - 0.0816P = 0.0184P
Loss% =× 100 = 1.84%

Test Level 2: Simple & Compound Interest - 2 - Question 16

A lent B Rs. 900 for a certain time at a certain rate per annum which was equal to the square root of the number of months of time. After the time, B wanted to return the money, but A instead of taking the interest, which amounted to Rs. 48, asked for a certain sum of money at the same rate for a certain number of years which was equal to the square root of the rate. Find the sum of money so that neither of them ends up as a loser. (Take simple interest)

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 16

A → B = Rs. 900
Let time = T years
Rate of interest = r%

⇒ r = 4%

B → A = Rs. P
Rate of interest = r = 4%
Time = T = 2 years

P = Rs. 600

Test Level 2: Simple & Compound Interest - 2 - Question 17

The simple interest on a certain sum at a certain rate is 9/16 of the sum. Find the rate of interest if its percentage value is equal to time in years.

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 17

Let the principal be P.
Suppose R = T = x

Test Level 2: Simple & Compound Interest - 2 - Question 18

A property decreased in value every year at the rate of on its value at the beginning of that year. If its value at the end of 3 years was Rs. 21,093.75, what was its worth at the beginning of these years?

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 18

Let the original value of the property be 'P'.
Using the formula: 

Hence, required answer = Rs. 25,600

Test Level 2: Simple & Compound Interest - 2 - Question 19

A sum of money is invested at compound interest at a certain rate. If the simple interest at the same rate is calculated, then the simple interest for the first two years comes out to be Rs. 20 less than the compound interest for the same number of years, and that for the first three years, comes out be Rs. 61 less than the compound interest for the same number of years. Find the rate.

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 19

Let principal = P. rate = R
According to question,
For 2 years,
C.I. - S.I. = 20

For 3 years,
C.I. - S.I. = 61

Dividing (1) and (2), we get

R = 5%

Test Level 2: Simple & Compound Interest - 2 - Question 20

If the difference between the compound interest and simple interest on a certain sum of money is Rs. 72 at 12% annum for 2 years, find the amount.

Detailed Solution for Test Level 2: Simple & Compound Interest - 2 - Question 20

Let the principal = x
Simple interest =
Compound interest = x 
So,

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