Question

Sammy lend altogether Rs 10,000 to James and Sophie for 2 years. James agrees to pay simple interest at 12% p.a and Sophie agrees to pay compound interest at the rate of 9% p.a. If Sophie paid Rs 596.70 more than James as the interest , find how much did he lend to each.

* Show your workings!

Help! Random/ Irrelevant answers will be reported!~​

Answer 1

Solution given;

let the amount given to James be x.

and to Sophie be 10,000-x.

now

for James

rate (r)=12%

time (t)=2 years

principal (p)=x

Simple interest=
`(p*t*r)/(100)=(x*12*2)/(100)=0.24x`

again

for Sophie

principal (p)=Rs 10,000-x

rate=9%

time(t)=2years

Compound interest=
`P[(1+(r)/(100))^(t)-1]`

=
`(10,000-x)[(1+(9)/(100))^2-1]`

=
`(10,000-x)[1.1881-1]`

=10,000*0.1881-0.1881x

=1881-0.1881x

Since

Sophie paid Rs 596.70 more than James as the interest

so

James interest +Rs596.70=Sophie's interest

0.24x+596.70=1881-0.1881x

0.24x+0.1881x=1881-596.70

0.4281x=1284.3

x=
`(1284.3)/(0.4281)=3000`

now

10,000-x=10,000-3000=Rs7000

He lended Rs 3000 to James

and

Rs 7000 to Sophie.

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