Answer

Correct Answer : d ) ₹ 405

Quick Approach

We know that,

Simple Interest=\(P×R×T \over 100\)

⇒For 2 year, 400=\(8000×R×2 \over 100\)

⇒ R = 2.5 %

We know that, for time 2 years

⇒CI-SI=\({SI ×R} \over {2×100}\)

⇒X-400= \({400×2.5} \over {2×100}\)

⇒ X = ₹ 405

Hence, (b) is the correct answer.

Basic Approach

Let sum be P, rate be R and time be T years.

Given, P = ₹ 8000, Simple interest (SI) = ₹ 400, compound interest (CI) = ₹ X, time = 2 years

We know that,

Simple Interest=\(P×R×T \over 100\)

400=\(8000×R×2 \over 100\)

⇒ R = 2.5 %

We also know that,

Compound interest =\( P×[(1+{R \over 100})^T-1]\)

⇒X = \(8000×[(1+{2.5 \over 100})^2-1]\)

⇒X=\(8000×({81 \over 1600})\)

⇒ X = ₹ 405

Hence (d) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA, UP SI etc.

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