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SSC Selection Post 2022 PYQ — Question 64

SSC Selection Post - Higher Secondary Level 2022 - 15 March 2022 - Shift 2 • Quantitative Aptitude • Q64

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A certain sum invested at simple interest amounts to Rs.10,072 in 3123{{1} \over 2} years and to Rs.11,552 in 6 years at the same rate per annum. The rate of interest p.a. is:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 7.4%.

Difference in time = 6 − 3.5 = 2.5 years, Difference in amount = ₹11,552 − ₹10,072 = ₹1,480

₹1,480=P⋅R⋅2.5100⇒P⋅R=59,200(1)₹1{,}480 = \frac{P \cdot R \cdot 2.5}{100} \quad \Rightarrow \quad P \cdot R = 59{,}200 \quad \text{(1)}

From the amount of 3.5 years:

10,072=P+P⋅R⋅3.5100\quad 10{,}072 = P + \frac{P \cdot R \cdot 3.5}{100}   

⇒3.5100⋅P⋅R=2,072⇒P=₹8,000\Rightarrow \frac{3.5}{100} \cdot P \cdot R = 2{,}072 \quad \Rightarrow P = ₹8{,}000

8,000⋅R=59,200⇒R=59,2008,000=7.4%\quad 8{,}000 \cdot R = 59{,}200 \quad \Rightarrow \quad R = \frac{59{,}200}{8{,}000} = \boxed{7.4\%}