Question:
Ramu has several friends and all of them are well settled in India. 1/5th of Ramu's friends went to Mumbai and 1/3rd of his friends went to Delhi. Three times the difference of these two went to Chennai, and only one went to Pune. How many of his friends went to Mumbai?
Ramu has several friends and all of them are well settled in India. 1/5th of Ramu's friends went to Mumbai and 1/3rd of his friends went to Delhi. Three times the difference of these two went to Chennai, and only one went to Pune. How many of his friends went to Mumbai?
Updated On: Aug 21, 2026
- 15
- 3
- 10
- Cannot be determined
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The Correct Option is B
Approach Solution - 1
1. The number of friends who went to Mumbai = \( \frac{T}{5} \)
2. The number of friends who went to Delhi = \( \frac{T}{3} \)
3. The number of friends who went to Chennai = 3 * (Difference between Delhi and Mumbai) = \( 3 \left( \frac{T}{3} - \frac{T}{5} \right) = 3 \left( \frac{5T - 3T}{15} \right) = 3 \left( \frac{2T}{15} \right) = \frac{6T}{15} = \frac{2T}{5} \)
4. The number of friends who went to Pune = 1
So, we can write the total as:
\[ T = \frac{T}{5} + \frac{T}{3} + \frac{2T}{5} + 1 \]
Combining like terms:
\[ T = \frac{T}{5} + \frac{2T}{5} + \frac{T}{3} + 1 \]
\[ T = \left( \frac{T + 2T}{5} \right) + \frac{T}{3} + 1 \]
\[ T = \frac{3T}{5} + \frac{T}{3} + 1 \]
To solve for \( T \), we find a common denominator for the fractions:
\[ T = \frac{9T + 5T}{15} + 1 \]
\[ T = \frac{14T}{15} + 1 \]
Multiplying both sides by 15 to clear the fraction:
\[ 15T = 14T + 15 \]
Solving for \( T \):
\[ T = 15 \]
The number of friends who went to Mumbai is:
\[ \frac{T}{5} = \frac{15}{5} = 3 \]
Therefore, the correct answer is option b) 3.
2. The number of friends who went to Delhi = \( \frac{T}{3} \)
3. The number of friends who went to Chennai = 3 * (Difference between Delhi and Mumbai) = \( 3 \left( \frac{T}{3} - \frac{T}{5} \right) = 3 \left( \frac{5T - 3T}{15} \right) = 3 \left( \frac{2T}{15} \right) = \frac{6T}{15} = \frac{2T}{5} \)
4. The number of friends who went to Pune = 1
So, we can write the total as:
\[ T = \frac{T}{5} + \frac{T}{3} + \frac{2T}{5} + 1 \]
Combining like terms:
\[ T = \frac{T}{5} + \frac{2T}{5} + \frac{T}{3} + 1 \]
\[ T = \left( \frac{T + 2T}{5} \right) + \frac{T}{3} + 1 \]
\[ T = \frac{3T}{5} + \frac{T}{3} + 1 \]
To solve for \( T \), we find a common denominator for the fractions:
\[ T = \frac{9T + 5T}{15} + 1 \]
\[ T = \frac{14T}{15} + 1 \]
Multiplying both sides by 15 to clear the fraction:
\[ 15T = 14T + 15 \]
Solving for \( T \):
\[ T = 15 \]
The number of friends who went to Mumbai is:
\[ \frac{T}{5} = \frac{15}{5} = 3 \]
Therefore, the correct answer is option b) 3.
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Approach Solution -2
Since the answer options already give possible values for the number of friends who went to Mumbai, each option can be tested directly by working out what the total number of friends would have to be, then checking whether all the given fractions and the one friend who went to Pune actually add up to that total.
- Option A (15 friends to Mumbai): If Mumbai's share of one-fifth of the total equals 15, the total would be 75 friends, so Delhi's share of one-third would be 25, and Chennai's share, three times the difference of 25 and 15, would be 30. Adding \( 15 + 25 + 30 + 1 = 71 \), which is not 75, so this option fails.
- Option B (3 friends to Mumbai): If Mumbai's share of one-fifth of the total equals 3, the total would be 15 friends, so Delhi's share of one-third would be 5, and Chennai's share, three times the difference of 5 and 3, would be 6. Adding \( 3 + 5 + 6 + 1 = 15 \), which exactly equals the assumed total of 15, so this option is consistent.
- Option C (10 friends to Mumbai): If Mumbai's share of one-fifth of the total equals 10, the total would be 50 friends, but then Delhi's share, one-third of 50, is not a whole number of friends, so this option fails.
- Option D (Cannot be determined): Since option B is fully consistent with every condition, the number of friends can in fact be determined, so this option is incorrect.
Only assuming 3 friends went to Mumbai makes every condition add up correctly to the same total.
the correct answer is Option B: 3.
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