A right circular cylindrical tank of radius 'R' meters and height (R + 7) meters contains oil. The entire quantity of oil is taken out from the cylindrical tank and poured into 'N' number of hemispherical bowls, such that each bowl is filled with its maximum capacity. If the maximum capacity of each bowl is 11R3 /42 m3 , then which of the following (i, ii, iii, and iv) are the possible values of 'N'? (R and N are positive integers).
i. 13
ii. 8
iii. 16
iv. 17
This questions was previously asked in
IBPS PO Mains (26th November 2022)
Only i and ii
Incorrect AnswerOnly i, ii, and iv
Incorrect AnswerOnly i and iii
Correct AnswerOnly iii
Incorrect AnswerNone of these
Incorrect AnswerExplanation:
Let’s break it down:
- The volume of the cylindrical tank is pR²(R+7).
- The volume of one hemispherical bowl is (11R³)/42.
- So, the number of bowls, N = [pR²(R+7)] / [(11R³)/42] = [42p(R+7)]/(11R), keeping R as a positive integer.
- This means N has to be a whole number, so 42p(R+7) must be divisible by 11R.
- p, as we use standard values, means 22/7. Substitute that in:
N = [42 × 22/7 × (R+7)] / (11R) = [132(R+7)]/(11R) = 12(R+7)/R.
Now let’s check the options:
- i. N = 13
- 12(R+7)/R = 13 ? 12R+84 = 13R ? R = 84.
- R is an integer. Possible.
- ii. N = 8
- 12(R+7)/R = 8 ? 12R+84 = 8R ? 4R = -84 ? R = -21.
- R can’t be negative. Not allowed.
- iii. N = 16
- 12(R+7)/R = 16 ? 12R+84 = 16R ? 84 = 4R ? R = 21.
- R is positive integer. Possible.
- iv. N = 17
- 12(R+7)/R = 17 ? 12R+84 = 17R ? 84 = 5R ? R = 16.8.
- R is not an integer. Not possible.
So only i and iii work.
Correct Answer:
Option: 3 — Only i and iii are possible values for N.
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By: Parvesh Mehta