A sum of Rs. 10 is lent by a child to his friend to be returned in 11 monthly instalments of Rs. 1 each, the interest being simple. The rate of interest is: 

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SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 2)
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  1. \(11{ 9 \over 11}\)%
  2. \(21{ 9 \over 11}\)%
  3. \(10{ 2 \over 11}\)%
  4. \(9{ 1 \over 11}\)%

Answer (Detailed Solution Below)

Option 2 : \(21{ 9 \over 11}\)%
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
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Detailed Solution

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Given:

A sum of Rs. 10 is lent by a child to his friend to be returned in 11 monthly instalments of Rs. 1 each, the interest being simple. 

Concept used:

Simple Interest, SI = (P × R × T)/100

Amount = P + SI

where

P = Principal amount

R = Rate of interest per year

T = Time in years

Calculation:

Let the rate of interest be R% p.a.

Total interest paid = 11 - 10  = Rs. 1

Since the installments are being paid monthly, the first, second, ...., and second-last EMI will incur interest for the next 10, 9, ...., and 1 month respectively. Since the last EMI completes the repayment, it will not incur any interest.

According to the concept,

(1 × R/100 × 10/12) + (1 × R/100 × 9/12) + (1 × R/100 × 8/12) + .... + (1 × R/100 × 1/12) = 1

⇒ \(\frac {R}{1200}\) (10 + 9 + ... + 1) = 1

⇒ \(\frac {R}{1200} \times \frac {11 \times 10}{2}\) = 1

⇒ R = 1200/55

⇒ R = \(21{ 9 \over 11}\)%

∴ The rate of interest is \(21{ 9 \over 11}\)%.

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