XAT 2020 — QA & DI Question 14
A box contains 6 cricket balls, 5 tennis balls and 4 rubber balls. Of these, some balls are defective. The proportion of defective cricket balls is more than the proportion of defective tennis balls but less than the proportion of defective rubber balls. Moreover, the overall proportion of defective balls is twice the proportion of defective tennis balls. What BEST can be said about the number of defective rubber balls in the box?
Answer & solution
It is exactly 3
- B
It is either 3 or 4
- C
It is exactly 2
- D
It is either 2 or 3
- E
It is either 0 or 1
Let the number of defective cricket, tennis and rubber balls = c, t and r respectively.
Given, r/4 > c/6 > t/5 ...(1)
and (c + t + r)/15 = 2 × t/5
⇒ c + r = 5t
Also, maximum value of c + r can be 5 + 4 = 9
⇒ The value of t can only be 1.
⇒ c + r = 5 …(2)
The only possible value to satisfy (1) and (2) is r = 3 and c = 2.
Hence, option (a).