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SSC GD 2024 PYQ — Question 42

SSC GD Const (English) - 22 Feb 2024 - Shift 3 • Quantitative Aptitude • Q42

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A certain sum of money becomes 3.5 times of itself in 14 years at a rate of simple interest. In 28 years, that amount it will become how many times of itself at the same rate of simple interest?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 6.

The principal amount = ( P)

The rate of interest = ( r ) per year.

amount = ( A)

⇒ A = P(1+rt100)P \left(1 + \frac{r t}{100}\right)

The amount after 14 years is:

⇒ A = 3.5P

⇒ 3.5P = P(1+r×14100)P \left(1 + \frac{r \times 14}{100}\right)

⇒ 3.5 = 1+14r100 1 + \frac{14r}{100}

⇒ 2.5 = 14r100\frac{14r}{100}

⇒ 250 = 14r

⇒ r = 25014=17.857\frac{250}{14} = 17.857  per year

The amount after 28 years is:

⇒ A = P(1+r×28100)P \left(1 + \frac{r \times 28}{100}\right)

⇒ A = P(1+17.857×28100)P \left(1 + \frac{17.857 \times 28}{100}\right)

⇒ 17.857×28100=500100=5\frac{17.857 \times 28}{100} = \frac{500}{100} = 5

⇒A = P (1 + 5) = P  × 6

 the answer is (6)