Question

Rs 2250 is divided among three friends Amar, Bijoy and Chandra in such a way that $\frac{1}{6}th$ of Amar's share, $\frac{1}{4}th$ of Bijoy's share and $\frac{2}{5}th$ of Chandra's share are equal. Find Amar's share.

• A. Rs 720
• B. Rs 1080
• C. Rs 450
• D. Rs 1240

Answer 1

The correct option is B Rs 1080

According to question,
$\frac{A}{6}=\frac{B}{4}=\frac{2C}{5}$
Multiplying all three fractions by LCM(6, 4, 5), we get
10A = 15B = 24C
Hence, $A+\frac{2A}{3}+\frac{5A}{12}=2250$
On solving, Amar's share = Rs.1080

Alternative Approach:
Amar's share should be divisible by 6. Option d gets rejected by this logic.
Further: A + B + C = 2250. If Amar's share is 720 (acc. To option a) Bijoy's share should be 480 & Chandra's share should be 300. (Gives us a total of 720 + 480 + 300 = 1500).
But the required total is 2250 (50% more than 1500). Since all relationships are linear, 1500 will increase to 2250 if we increase all values by 50%. Hence, Amar's share should be 1080.