Question

A certain sum of money amounts to Rs 1008 in 2 years and to Rs 1164 in 3 ½ years. Find the sum and the rate of interest.

Answer 1

We know that:

Simple interest for 1 ½ years:

$\implies$ Rs. (1164 - 1008)

$\implies$ Rs. 156

Simple interest for 2 years:

$\implies$ Rs. (156 × 23 × 2)

$\implies$ Rs. (156 × 46)

$\implies$ Rs. 208

Principal:

$\implies$ Rs. (1008 - 208)

$\implies$ Rs. 800

Now:

P = 800, T= 2, S.I. = 208

Therefore:

$\implies$ Rate = (100 × S.I.) / (P × T)

$\implies$ Rate = [ (100 × 208)/(800 × 2)]

$\implies$ Rate = [ (20800)/(1600)]

$\implies$ Rate = 13%

Final answer: 13%

Answer 2

Answer:

for 2 yr sum is Rs. 1008

for 3.5 yr sum is Rs. 1164

S.I for 1.5 yrs = 1164-1008=156

S.I for 2 yrs = 156×(2/3)×2=208......(i)

Now principal value = 1008-208 = 800.....(ii)

Now rate of interest for 2 yrs is given by

rate = (S.I. × 100)/( Principal value × Time)

= (208×100)/(800×2)

= 13 •/•