Question

A sum of money at simple interest amounts to rs.4480 in 2years and rs. 5200 in 5 years.what is the original sum?

Answer 1

Answer:

2 years =4480

5years=5200

the original sum is= 9,680

Answer 2

The original sum is Rs. 4000.

• A sum of money at simple interest amounts to Rs. 4480 in 2 years and Rs. 5200 in 5 years.

• The formula to find the simple interest is

I = P×N×R/100

• We substitute the given information,

I₁ = P×2×R/100          

I₂ = P×5×R/100          

• Now,

4480 = P + I₁

4480 = P +  P×2×R/100

P = $\frac{4480}{(1+\frac{2R}{100})}$     (Equation 1)

• And 5200 = P + I₂

5200 = P +  P×5×R/100

P = $\frac{5200}{(1+\frac{5R}{100})}$     (Equation 2)

• Equating equation 1 and 2

$\frac{4480}{(1+\frac{2R}{100})}$ = $\frac{5200}{(1+\frac{5R}{100})}$

$\frac{4480}{5200}$ = $\frac{(1+\frac{2R}{100})}{(1+\frac{5R}{100})}$

$\frac{56}{65}$ = $\frac{100+2R}{100+5R}$

5600+280R = 6500+130R

150R = 900

R = 6%p.a.

• The rate of interest is 6 p.c.p.a.
• Now substituting the value of r in the equation 1 , we get

P = $\frac{4480}{(1+\frac{2R}{100})}$

P = $\frac{4480}{(1+\frac{12}{100})}$

P = $\frac{448000}{112}$ =4000

• The principal amount is Rs. 4000