Question

gagan invests some money at a certain rate for 3 years and gets an amount of $7965.if he invests the same amount at the same amount at the rate for 5years 6months,he will get an money of $8977.50. calculate the sum he invests and the rate of interests?

Answer 1

Hi ,

1 ) Let principal = Rs x

Rate of interest = r %

Time = t = 3 yrs

Amount ( A1 ) = Rs 7965

*****************************************

A = P ( 1 + TR/100 )

******************************************

7965 = x( 1 + 3r/100 )

7965 = x( 100+ 3r )/100

796500 = x ( 100 + 3r ) ---( 1 )

2 ) principal = Rs x

Rate of interest = r%

Time = 5½ = 11/2 years

Amount ( A2 ) = Rs 8977.50

8977.50 = x( 1 + 11r/200 )

8977.50 × 200 = x( 200 + 11r )

1795500 = x( 200 + 11r )---( 2 )

Find the ratio of ( 2 ) and ( 1 ) , we

get ,

133/59 = ( 200 + 11r)/( 100 + 3r )

133( 100 + 3r ) = 59( 200 + 11r )

13300 + 399r = 11800 + 649r

13300 - 11800 = 649r - 399r

1500 = 250r

1500/250 = r

6 = r

Therefore ,

r = 6%

Substitute r = 6% in equation ( 1 ) ,


we get ,

7965 = x ( 100 + 18)/100

( 7965 × 100 )/118 = x

Rs6750 = x

Principal = Rs x = Rs 6750

I hope this helps you.

: )

Answer 2

Given:

Amount after 3 years = 7965 Rs

Amount after 11/2 years= 8977.50 Rs

Then,interest for 5/2 years= Rs 8977.50- Rs 7965

= 1012.50 Rs

Then,interst for 1 year= 1012.50\2.5

= 405 Rs

Now,S.I for 3 years = 405•3

=1215 Rs

Therefore, Principal= Rs 7965 - Rs1215

= Rs 6750

As we now know the principal i.e 6750

Rate of interest= SI • 100/P•T

i.e 1215•100/6750•3

= 6% p.a.