Question

The difference between simple interest and compound interest on a certain sum is ₹54, 40 for 2 years at 8 percent per annum. Find the sum.
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Answer 1

Given :–

• Difference between S.I. (Simple Interest) and C.I. (Compound Interest) = Rs. 54.40
• Time = 2 years
• Rate = 8% per annum

To Find :–

• The sum.

Solution :–

● Simple Interest (S.I.) for 2 years = $\dfrac{P \times R \times T}{100}$

⟹ $\sf \dfrac{P \times 8 \times 2}{100}$

Cut the denominator and the numerator by 2, we obtain

⟹ $\sf \dfrac{P \times 4 \times 2}{50}$

Again, cut the denominator and the numerator by 2, we obtain

⟹ $\sf \dfrac{P \times 2 \times 2}{25}$

⟹ $\sf \dfrac{P \times 4}{25}$

⟹ $\sf \dfrac{4P}{25}$

• $\sf \dfrac{4P}{25}$

● Compound Interest (C.I.) = P ${ ( 1 + \sf \dfrac{R}{100} )}^{2}$ – P

• n = time.

⟹ P $\sf { (1 + \dfrac{8}{100})}^{2}$ – P

Cut the denominator and the numerator by 2, we obtain

⟹ P $\sf {(1 + \dfrac{4}{50})}^{2}$ – P

Again, cut the denominator and the numerator by 2, we obtain

⟹ P $\sf {(1 + \dfrac{2}{25})}^{2}$ – P

⟹ P $\sf {(\dfrac{27}{25})}^{2}$ – P

⟹ P $\sf (\dfrac{729}{625})$ – P

⟹ $\sf \dfrac{729P}{625}$ – P

• $\sf \dfrac{729P}{625}$

C.I. – S.I. = 54.40 [Given]

⟹ 54.40 = $\sf \dfrac{729P}{625}$ – $\sf \dfrac{4P}{25}$

L.C.M. of the denominators (625, 25) = 625.

⟹ 54.40 = $\sf \dfrac{729P - 625P - 100P}{625}$

⟹ 54.40 = P $\sf (\dfrac {729 - 625 - 100}{625})$

⟹ 625 × 54.40 = P (104 - 100)

⟹ 625 × 54.40 = P (4)

⟹ 625 × 54.40 = 4P

⟹ $\sf \dfrac{625 \times 54.40}{4}$ = P

⟹ $\sf \dfrac{34000}{4}$ = P

Cut the denominator and the numerator by 2, we obtain

⟹ $\sf \dfrac{17000}{2}$ = P

Again, cut the denominator and the numerator by 2, we obtain

⟹ 8500 = P

• P = Rs. 8,500
• C.I. – S.I. = Rs. 54.40

Then, the sum is,

⟹ P × (C.I. – S.I.)

⟹ 8,500 × 54.40

⟹ 4,62,400

Hence,

The sum is Rs. 4,62,400.