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An office receptionist took Rs. 8000 as a personal loan from the manager for 6 months at 11% p.a. simple interest. At the end of six months, she gave the manager an Rs. 3500 and a gold coin to settle her dues. At what price did the manager get the gold coin?

Last updated date: 13th Jun 2024
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372.6k+ views
Hint: In the above question you were asked to find the price of the gold coin which the receptionist has paid. For solving this question, you will need to use the formula of simple interest. After finding the simple interest you will have to find the amount. So, let us see how we can solve this problem.

Complete Step by Step Solution:
In this question we have:
Principle(P) = Rs. 8000
Rate(R) = 11%
Time(T) = 6 months
In the formula of simple interest, we write time in terms of years. Here, we have 6 months, so $\dfrac{1}{2}$ years.
The formula of simple interest is: $\dfrac{{P \times R \times T}}{{100}}$ .
Putting the values of P, R and T in the formula of simple interest we get
 $= \dfrac{{8000 \times 11 \times \dfrac{1}{2}}}{{100}}$
 $= \dfrac{{4000 \times 11 \times 1}}{{100}}$
After solving the above expression we get,
 $= 440$
Therefore, S.I = Rs. 440
Amount = Principle + S.I
Therefore, Amount = Rs. (8000+440)
= Rs. 8440
Therefore, after 6 months receptionist has to pay Rs. 8440
It is given in the question that receptionist has paid Rs. 3500, so the price of gold coins will be
= Rs. (8440 - 3500)
= Rs. 4900

Therefore, the price of gold coins which the receptionist has paid is Rs. 4900.

In the above solution we used the formula of simple interest and then we calculated the total amount which the receptionist has to pay after 6 months. After which we subtracted Rs. 3500 that the receptionist has already paid. And for the rest of the amount, she gave the gold terms, which should be equal to the remaining amount. So we get to know that the price of the gold coin should be equal to the remaining money after payment of Rs. 3500.