Question 147

A certain number of capsules were purchased for Rs. 216. Fifteen more capsules could have been purchased in the same amount if each capsule was cheaper by Rs.10 What, was the original number of capsules purchased ?

Solution

cost of 1 capsule = Rs. x
Total capsules purchased = n

According to the question :-
n*x = 216..........................(1)
(n+15)*(x-10) = nx
nx + 15x - 150 - 10n = nx
3x - 2n = 30
x = $$\frac{30+2n}{3}$$

substituting x in eqn (1)
$$\frac{30+2n}{3}$$ * n = 216
30n + 2$$n^2$$ = 648
(n+27)(n-12) = 0
n =12

originally 12 capsules were purchased

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