Question

Jyoti investigation at 10% per annum for 2 years at simple interest and Arya invest the same some for the period interest but compounded annually if Arya gets 150 more than Jyoti find the sum invested by each of them

Answer 1

Answer:

15,000

Step-by-step explanation:

Let the sum invested by each person = p

Jyoti invests at simple interest, so she receives :

p + $\frac{p X r X t}{100}$

= p + $\frac{p X 10 X 2}{100}$

= p + $\frac{p}{5}$

= $\frac{6p}{5}$

= 1.2p          . . . (1)

Arya invests at interest compunded annually (number of periods = 2) so she receives :

p X $(1 + \frac{i}{100})^{n}$

= p X $(1 + \frac{10}{100} )^{2}$

= 1.21p          . . . (2)

Arya earns 150 more than Jyoti, so

1.21p = 1.2p + 150

⇒ 1.21p - 1.2p = 150

⇒ 0.01p = 150

⇒ p = $\frac{150}{0.01}$ = 15,000

Hence, both of them invested 15,000