Question

Find the principal if the difference between C.I and S.I on it at 15% p.a for 3 years is ₹ 1134.

• A. ₹ 16000
• B. ₹ 18000
• C. ₹ 20000
• D. ₹ 22000

Answer 1

The correct option is A ₹ 16000

Given:
Difference between Compound Interest (C.I.) and Simple Interest (S.I.) = ₹ 1134
Rate of interest, R = 15%
Number of years = 3
Principal amount, P = ?

Now,

S.I. = (P $\times$ R $\times$ T)/100

S.I. = (P $\times$ 15 $\times$ 3)/100 -----(1)

C.I. = Amount - Principal

= P ( 1 + (R/100))${}^n$ - P

C.I. = P( 115/100)${}^3$ - P -------(2)

C.I. - S.I. = 1134 -------(3)

By substituting values of C.I. and S.I. in equation (3), we get

P( 115/100)${}^3$ - P - (P$\times$15$\times$3)/100 = 1134

$\Rightarrow$ P[ (115/100)${}^3$ - 1 - (45/100)] = 1134

$\Rightarrow$ P [(23/20)${}^3$ - 29/20] = 1134

$\Rightarrow$ P (567/8000) = 1134

$\Rightarrow$ P = 2 $\times$ 8000

$\Rightarrow$ P = 16000

Hence, the principal amount is ₹ 16,000