Question

One year payment to the servant is Rs. 90 plus one gift coupon. The servant leaves after 9 months and receives Rs. 65 and a gift coupon. Determine the value of the gift coupon?

• A. Rs. 7.50
• B. Rs. 15
• C. Rs. 10
• D. Rs. 12
• E. Rs. 18

Hint:

The coupon is received at the end of the service period, so it's included in both yearly and partial payments.

Answer 1

The Correct Option is C

Step 1: Let the value of gift coupon = \(x\).
Yearly payment = \(90 + x\).
Monthly payment = \(\frac{90 + x}{12}\).

Step 2: Payment for 9 months:
\[ 9 \times \frac{90 + x}{12} = 65 + x \]
Multiply both sides by 12:
\[ 9(90 + x) = 12(65 + x) \]
\[ 810 + 9x = 780 + 12x \]
\[ 810 - 780 = 12x - 9x \]
\[ 30 = 3x \]
\[ x = 10 \]