QUESTIONS ON SIMPLE INTEREST (PART-II)

QUERY 11

The difference between the simple interest received from two different sources on Rs 1500 for 3 years in Rs 13.50. The difference between their rates of interest is?

A) 0.1%
B) 0.2%
C) 0.3%
D) 0.4%

MAHA GUPTA
Difference of interest for 1 year = ^13.50⁄₃ = 4.5 = ⁹⁄₂

This difference is on Rs 1500, so to find the rate of interest we must calculate it on Rs 100 as the rate of interest is on 100 unless stated otherwise

Therefore on Rs 100, the difference of interest = (⁹⁄₂)(1/1500)100= ³⁄₁₀ = 0.3

Hence difference of rate of interest = 0.3% (option ‘C’)

QUERY 12

A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. Find the sum.

A) Rs. 650
B) Rs. 690
C) Rs. 698
D) Rs. 700

MAHA GUPTA
If interest of e years is deducted from the amount of Rs 815, the problem is solved.

Now interest for 1 year = 854 – 815 = 39

Thus interest for 3 years = 39 × 3 = 117

Therefore the sum of money (principal) in the beginning = 815 – 117 = Rs 698 (option ‘C’)

QUERY 13

Rohan invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in scheme B?

A) Rs. 6400
B) Rs. 6500
C) Rs. 7200
D) Rs. 7500

MAHA GUPTA
Let the sum invested in Scheme A be Rs x
Thus, the sum invested in scheme B be Rs (13900 – x)

Now interest on Rs x = (x*14*2)/100
And interest on Rs (13900 – x) = [(13900 – x)*11*2]/100

Now, according to the question
(x*14*2)/100 + [(13900 – x)*11*2]/100 = 3508
=> x = 7500

So, the amount invested in scheme B = 13900 – 7500 = Rs 6400 (option ‘A’)

QUERY 14

Reena took a loan of Rs 1200 with simple interest for as many years as the rate of interest. If she paid Rs 432 as interest at the end of the loan period, what was the rate of interest?

A) 3.6
B) 6
C) 18
D) 7

MAHA GUPTA
Let rate = r%
Thus, time = r years.

Now according to question
(1200*r*r)/100 = 432
=> 12r² = 432
=> r = 6 (option ‘B’)

QUERY 15

A financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes?

A) 10%
B) 10.25%
C) 10.5%
D) 11%

MAHA GUPTA
Let money lent Rs 100

Therefore interest for the first 6 months of the year = Rs. (100*10*1)/(100*2) = Rs 5
100 x 2

Thus principal in the beginning of the second 6 months of the year = 100 + 5 = 105
And interest for the second 6 months of the year = Rs. (105*10*1)/(100*2) = Rs 5.25

So, amount at the end of 1 year = 100 + 5 + 5.25 = Rs 110.25

Hence, the effective rate of interest = 110.25 – 100 = 10.25% (option ‘B’)

QUERY 16

Find the rate at simple interest, at which a sum becomes four times of itself in 15 years.

A) 10%
B) 20%
C) 30%
D) 40%

MAHA GUPTA
Let the sum = Rs 100
Thus, amount after 15 years = Rs 100*4 = Rs 400

Hence the interest in 15 years = 400 – 100 = Rs 300
Therefore, interest in 1 year = 300/15 = Rs 20

But this interest is on Rs 100, hence rate of interest = 20% (option ‘B’)

QUERY 17

What is the present worth of Rs 132 due in 2 years at 5% simple interest per annum?

A) Rs 110
B) Rs 120
C) Rs 130
D) Rs 140

MAHA GUPTA
We have to remember that Rs 132 here is not the principal, rather it is the amount i.e. ‘principal+ interest’

Now let the present worth i.e. principal = Rs 100

Thus, interest on this sum in 2 years at 5% per annum = (100*5*2)/100 = Rs 10
And the amount due in the end = 100 + 10 =110

If the amount due is 110, the present worth = 100
If the amount due is 132, the present worth = (100/110)*132 = Rs 120 (option ‘B’)

QUERY 18

The simple interest on a certain sum of money at the rate of 5% p.a. for 8 years is Rs 840. At what rate of interest the same amount of interest can be received on the same sum after 5 years?

A) 5%
B) 6%
C) 7%
D) 8%

MAHA GUPTA
Here firstly we need to calculate the principal amount, then only we can calculate the new rate.

Now, r = 5%, time = 8 years, interest = Rs 840
Hence, the principal = (100*840)/(5*8) = Rs 2100

Hence new rate of interest = (100*840)/(5*2100) = 8% (option ‘D’)

QUERY 19

Rs 800 become Rs 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4%, what amount will Rs 800 become in 3 years?

A) Rs 1052
B) Rs 1152
C) Rs 1252
D) Rs 1352

MAHA GUPTA
Interest in the first case = 956 – 800 = Rs 156

Therefore the rate of interest = (156∗100)/(800∗3) = 6½%
As the principal and time are same we do not need to find the new rate of interest, only the increase in the rate of interest will be enough.

Now, the increase in the rate of interest = 4%
Hence, increase in the interest = (800*4*3)/100 = Rs 96

So, total interest = 156 + 96 = Rs 252

Therefore the required amount = 800 + 252 = Rs 1052 (option ‘A’)

QUERY 20

A certain sum amounts to Rs 7350 in 2 years and to Rs 8575 in 3 years. Find the sum and rate percentage?

A) Rs 4900;     25%
B) Rs 5900;     25%
C) Rs 4800;     35%
D) Rs 5400;     50/3%

MAHA GUPTA
When the manner of rate of interest is not given, it’s treated to be simple rate of interest. So if in the exam such is a question always take it as simple interest; not the compound interest. However, I’ll take it both ways just to show how to do in both the cases.

CASE-I (SIMPLE INTEREST)
Interest for 3rd year = amount of three years – amount of two years = 8575 – 7350 = 1225

Therefore interest for 2 years = 1225*2 = 2450
Hence the sum (principal) in the beginning = 7350 – 2450 = 4900

Now the principal = 4900; interest = 2450; time = 2 years

So rate of interest= ^{(interest *100)}⁄_{(principal*time)} = ^(2450*100)⁄_(4900*2) = 25%

So sum = 4900; Rate = 25% (option ‘A’)

CASE-II (COMPOUND INTEREST)
Remember, interest for 1 year is the same whether it’s simple interest or the compound interest

Now interest of third year = Amount after 3 three years – Amount after two years = 8375 – 7350 = 1225; means principal for this interest is 7350 if the rate of interest is compound.

If 7350 is the principal interest = 1225
If 100 is the principal interest = (¹²²⁵⁄₇₃₅₀)*100 = 50/3
Hence rate of compound interest = 50/3%

When a thing increases for two successive times at the same rate, the overall increase on initial amount = a + b + ^(a*b)⁄₁₀₀

Therefore overall interest for two years = 50/3 + 50/3 + ^{[(50/3)*(50/3)]}⁄₁₀₀ = 325/9%

Therefore amount after 2 years = 100 + 325/9 = 1225/9

If 1225/9 is the amount, the principal = 100
If 7350 is the amount, the principal = (⁹⁰⁰⁄₁₂₂₅)*7350 = 5400

So sum (principal) = 5400; Rate = 50/3% (answer)