If the difference of the compound interest and the simple interest on

1.	If the difference of the compound interest and the simple interest on a sum of money for 3 years is Rs.702 at 12% p.a., then the principal is:1. Rs.156252. Rs.180003. Rs.428754. Rs.31250
Answer» Correct Answer - Option 1 : Rs.15625 Given: C.I. - S.I. = Rs.702 ----(i) Rate (R) = 12% Time (T) = 3 years Formula used: S.I. = (P × R × T)/100 A = P(1 + R/100)n Where A → amount n → time S.I. → Simple Interest P → Principal R → Rate T → Time Calculations: Let the sum of money be Rs. P. According to the question, S.I. = (P × 12 × 3)/100 = 9P/25 ----(ii) Similarly, C.I. = P(1 + 12/100)³ - P ⇒ C.I. = P × (28/25) × (28/25) × (28/25) - P ⇒ C.I. = (21952P/15625) - P ⇒ C.I. = (6327P/15625) ----(iii) Putting values of C.I. and S.I. from (iii) and (ii) respectively in (i), We get, (6327P/15625) - (9P/25) = 702 ⇒ {(6327P - 5625P)/15625} = 702 ⇒ (702P/15625) = 702 ⇒ P = Rs.15625 ∴ The principal is Rs.15625.

If the difference of the compound interest and the simple interest on a sum of money for 3 years is Rs.702 at 12% p.a., then the principal is:1. Rs.156252. Rs.180003. Rs.428754. Rs.31250

Answer» Correct Answer - Option 1 : Rs.15625

Given:

C.I. - S.I. = Rs.702 ----(i)

Rate (R) = 12%

Time (T) = 3 years

Formula used:

S.I. = (P × R × T)/100

A = P(1 + R/100)n

Where A → amount

n → time

S.I. → Simple Interest

P → Principal

R → Rate

T → Time

Calculations:

Let the sum of money be Rs. P.

According to the question,

S.I. = (P × 12 × 3)/100 = 9P/25 ----(ii)

Similarly, C.I. = P(1 + 12/100)³ - P

⇒ C.I. = P × (28/25) × (28/25) × (28/25) - P

⇒ C.I. = (21952P/15625) - P

⇒ C.I. = (6327P/15625) ----(iii)

Putting values of C.I. and S.I. from (iii) and (ii) respectively in (i),

We get, (6327P/15625) - (9P/25) = 702

⇒ {(6327P - 5625P)/15625} = 702

⇒ (702P/15625) = 702

⇒ P = Rs.15625

∴ The principal is Rs.15625.

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