If Rs. 40 be allowed as true discount on a bill of Rs. 440

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If Rs. 40 be allowed as true discount on a bill of Rs. 440 at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is Rs. ?

1. 72.80
2. 73.32
3. 72.00
4. 73.20

Correct Option: C

As we know that ,
Present worth = Amount − True Discount = 110 − 10 = Rs. 100
SI on Rs. 100 for a certain time = Rs. 10
SI on Rs. 100 for double the time = Rs. 20
True Discount on Rs. 120 = 120 − 100 = Rs. 20
True Discount on Rs. 1 = 20/120
True Discount on Rs. 440 = 20 x 440/120 = 20 x 44/12 = 20 x 22 / 6 = 440 /6 = 73.2