Question

There are only two machines Alpha and Beta in Limestone Industries. It takes machine Alpha m hours to polish a granite stone that machine Beta can polish in n hours. If machine Alpha operates alone for p hours and is then joined by machine Beta until 100 stones are polished, for how long will the two machines operate simultaneously? Assume that all the granite stones are of identical size

• A. (100mn-p)/(m+n)
• B. n(100m-p)/(m+n)
• C. 100n (m-p)/(m+n)
• D. (m+n)/(100mn-p)

Answer 1

The correct option is B n(100m-p)/(m+n)

The easiest way to solve this question is by assuming simple values for m,n and p. Let m=1 and n=2 (i.e. Alpha takes 1 hour to polish a stone $\&$ Beta takes 2 hours to polish a stone)

Let p=10, Then after 10 hours, 10 stones are completed by Alpha. Together, in 1 hour Alpha and Beta complete $\frac{3}{2}$ stones

Hence to complete the remaining 90 stones, they need 60 hours.Look in the answer options for 60. Answer is option (b)