Question 7

Veena has to pay Rs. 2460 to Sita, 5 Months later at 6% SI per annum, and Gita has to pay Sita same amount at 7.5% SI per annum after certain months. If both took the same amount of loan from Sita then Gita paid loan after how many months?

Solution

Veena has to pay Rs. 2460 to Sita , which is the Amount. Let the principal be x, ie veena borrowed Rs x from Sita.

Then the SI = $$\dfrac{P\times\ r\times\ n}{100}=\frac{x\times\ \dfrac{5}{12}\times\ 6}{100}=\dfrac{x}{40}$$

So the total amount paid will be $$x+\dfrac{x}{40}=2460\ =>\ x=\dfrac{2460}{41}\times\ 40=2400$$

Hence, Veena borrowed Rs 2400 from Sita. Now, Gita also borrowed the same amount and paid the same amount but her interest rate was 7.5%.

So, thr Si paid by gita is 2460-2400=60; $$60=\frac{2400\times\ 7.5\times\ t}{100}$$ where t is the time for which the amount was borrowed.

Solving this, we get $$t=\frac{1}{3}\ years=\frac{1}{3}\times\ 12=4\ monthes$$

Hence, option B is the correct choice.

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