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?

• A. 15
• B. 3
• C. 10
• D. Cannot be determined

Answer 1

Answer: (B)

3

Answer 2

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.