A certain sum becomes ₹ 600 in a certain time at the rate of 6% simple interest. The same sum amounts to ₹ 200 at the rate of 1% simple interest in the same duration. Find the sum and time.

₹ 120 and 662/3 yr
₹ 150 and 662/3 yr
₹ 130 and 662/3 yr
₹ 160 and 662/3 yr

Correct Answer: ₹ 120 and 662/3 yr

Explanation:

According to the question.
([P + (P x 6 x T)/100] - [P + (P x 1 x T)/100] = 600 - 200
⇒ 5PT/100 = 400
⇒ PT = 8000
Again, for 6% rate,
SI = PTR/100 = (8000 x 6)/100 = ₹ 480
∴ Sum = 600 - 480 = ₹ 120
As we have, PT = 8000
∴ T = 8000/120 = 200/3 = 66²/₃ yr

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