Question

Kamal and Anand each lent the same sum of money for 2 years at 5% at simple interest and compound interst respectively. Anand recived Rs. 15 more than Kamal. Find the amount of money lent by each and the interest received.

Answer 1

Let principal = Rs. 100, R = 5% T = 2 years

For Kamal, SI = `[ 100 xx 5 xx 2 ]/100` = Rs. 10

For Anand,        `"A" = "P"[ 1 + "R"/100 ]^"T"` 

= `100[ 1 + 5/100]^2`

= `100 xx 21/20 xx 21/20`

= `441/4`

CI = `441/4 - 100 = 41/4`

Difference of CI and SI = `41/4 - 10`

= `[ 41 -40 ]/4`

= Rs. `1/4`

When difference is Rs.`1/4` , then principal = Rs. 100.
If difference is 1, principal = 100 x 4
If difference is Rs.15, principal = 100 x 4 x 15 = Rs. 6000

For kamal, interest = `[ 6000 xx 5 xx 2 ]/100` = Rs. 600.

For Anand, interest = `6000[ 1 + 5/100 ]^2 - 6000`

= `6000[ (21/20)^2 - 1 ]`

= `6000[ 441/400 - 1 ]`

= `6000 xx 41/400`

= Rs. 615