# (solved)Question 8 SSC-CGL 2018 June 4 Shift 1

An amount becomes 8,028 in 3 years at a fixed percentage interest rate and 12,042 in 6 years, when the interest is compounded annually. What is the actual amount?
(Rev. 03-Aug-2022)

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### Question 8SSC-CGL 2018 June 4 Shift 1

An amount becomes 8,028 in 3 years at a fixed percentage interest rate and 12,042 in 6 years, when the interest is compounded annually. What is the actual amount?

1. 5352
2. 5235
3. 5253
4. 5325

### Solution in Short

Periods of growth are 3 year each, so we can apply unitary method.

Observe that Re. 12042 is obtained from 8028 in three years.

Hence, Re. 8028 was obtained from:

$\displaystyle \frac{8028}{12042} \times 8028 = 5352 \text{ Rs. } \:\underline{Ans}$

### Solution in Detail

Use the CI formula on 8028, 3 years:

$\displaystyle 8028 = P \bigg(1 + r\bigg)^3 \text{ . . . (1)}$

Use the CI formula on 12042, 6 years:

$\displaystyle 12042 = P \bigg(1 + r\bigg)^6\text{ . . . (2)}$

Squaring (1), then dividing by (2):

$\displaystyle P = \frac{8028 \times 8028}{12042}$

Either calculate or conclude that P must be even. Hence (a) is the answer!

### Solution 3

In compound interest, percent growth is same for same periods of time.

$\displaystyle P \xrightarrow [\text{3 yrs}]{\times 1.5} 8028 \xrightarrow [\text{3 yrs}]{\times 1.5} 12042$

Hence P must be $\displaystyle \frac{2}{3} \times 8028= 5352$. Hence (a) is the answer!