## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 8 Simple and Compound Interest Ex 8.1

Question 1.

Find the simple interest on ₹4000 at 7.5% p.a. for 3 years 3 months. Also find the amount.

Solution:

Here, P (Principal) = ₹4000

R (rate of interest) = 7.5% p.a. = \(\frac{15}{2}\)% p.a

T (time) = 3 years 3 months

Amount = P + I = ₹14000 + ₹975 = ₹4975

Question 2.

What sum of money will yield ₹170·10 as simple interest in 2 years 3 months at 6% per annum?

Solution:

Here, I = ₹170·10, T = 2 years 3 months

= 2\(\frac{3}{12}\) years = 2\(\frac{1}{4}\) years

= \(\frac{9}{4}\) years

R = 6%

Question 3.

Find the rate of interest when ₹800 fetches ₹130 as simple interest in 2 years 6 months.

Solution:

Here, P = ₹800, I = ₹130

T = 2 years 6 months = 2\(\frac{6}{12}\) years

= \(\frac{13}{2}\) % p.a.= 6·5% p.a.

Question 4.

Find the time when simple interest on ₹3·3 lakhs at 6·5% per annum is ₹75075.

Solution:

Here, P = 3·3 lakhs = ₹3·3 × 100000 = ₹330000

R = 6·5% per annum

I= ₹75075

Question 5.

Find the sum of money when

(i) simple interest at 7\(\frac{1}{4}\)% p.a. for years is ₹2356·25

(ii) final amount is ₹ 11300 at 4% p.a. for 3 years 3 months.

Solution:

(i) Here, I = ₹2356·25

(ii) Amount (A) = ₹11300

Rate (R) = 4% p.a.

Time (T) = 3 years 3 months

Hence principal (P) = ₹10000

Question 6.

How long will it take a certain sum of money to triple itself at 13\(\frac{1}{3}\)% per annum simple interest?

Solution:

Let the sum of money = ₹ x

Amount = 3 × ₹ x = ₹ 3x

Interest = Amount – Principal = ₹3x – ₹x = ₹2x

Question 7.

At a certain rate of simple interest ₹4050 amounts to ₹4576·50 in 2 years. At the same rate of simple interest, how much would ₹1 lakh amount to in 3 years?

Solution:

Here, P = ₹4000, A = ₹4576·50,

T = 2 years

I = A – P = ₹4576·50 – ₹4050 = ₹526.50

Let the rate of simple interest be R% per annum

Amount = Principal + Interest = ₹100000 + ₹19500 = ₹119500

Question 8.

What sum of money invested at 7.5% p.a. simple interest for 2 years produces twice as much interest as ₹9600 in 3 years 6 months at 10% p.a. simple interest?

Solution:

In first case,

Principal (P_{1}) = ₹9600

Rate (R_{1}) = 10%

Period (T) = 3 years 6 months = \(3 \frac{1}{2}=\frac{7}{2}\) years

S. Interest = \(\frac{P R T}{100}=\frac{9600 \times 10 \times 7}{100 \times 2}\) = ₹3360

In second case,

S. Interest = ₹3360 × 2 = ₹6720

Rate (R) = 7.5% p.a.

and Period (T) = 2 years