An equal sum is invested in two different schemes. One scheme gives simple interest and the other gives compound interest (annual compoundi… — Answer & Discussion

An equal sum is invested in two different schemes. One scheme gives simple interest and the other gives compound interest (annual compounding). The sum of interest obtained after 2 years from both the schemes is Rs. 2961. If both schemes have 23% per annum interest rate, then what is the first year interest (in Rs.) of simple interest scheme?

A500
B1100
C700
D900

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Discussion 1

CCommunity22 May 2019

Let Rs. P be the principal.

According to the question,

(P × 23 × 2)/100 + P [(1 + 23/100)2 - 1] = 2961

⇒ 0.46P + 0.5129P = 2961

⇒ 0.9729P = 2961

⇒ P = 2961/0.9729

So, SI for 1 year = ((2961/0.9729) × 23 × 1)/100 = Rs. 700

Short trick:

Total percentage of SI in 2 years = 23 + 23 = 46%

And total percentage of CI in 2 years = 23 + 23 + (23 × 23)/100 = 51.29

According to question (CI + SI) = 46 + 51.29 = 97.29

⇒ 97.29 unit = 2961

∴ 23 unit = 2961/97.29 × 23 = 700