Suppose that one-third of a certain sum is invested at 3% simple interest, one-sixth is invested at 6% simple interest and the rest of the sum at 8%. If the annual amount is Rs. 600, then the original sum is:

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SJVNL ET Electrical 2019 Official Paper

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Answer 1

Given:

One-third of sum (S) invested at 3% simple interest

One-sixth of sum (S) invested at 6% simple interest

Rest of sum (S) invested at 8% simple interest

Total annual interest = ₹600

Formula used:

Simple Interest (SI) = P × R × T / 100

Where P = Principal, R = Rate of Interest, T = Time

Calculations:

Let the total sum be S.

1/3 of S invested at 3%, so interest = (1/3)S × 3 × 1 / 100 = S/100

1/6 of S invested at 6%, so interest = (1/6)S × 6 × 1 / 100 = S/100

Remaining amount = S - (1/3)S - (1/6)S = (1 - 1/3 - 1/6)S = (1 - 2/6 - 1/6)S = (1 - 3/6)S = (1/2)S

(1/2)S invested at 8%, so interest = (1/2)S × 8 × 1 / 100 = 4S/100

Total Interest = S/100 + S/100 + 4S/100 = ₹600

⇒ 6S / 100 = 600

⇒ S = 600 × 100 / 6

⇒ S = ₹10,000

∴ The correct answer is option (4).

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