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Question

Rs 2250 is divided among three friends Amar, Bijoy and Chandra in such a way that 16 th of Amar's share, 14 th of Bijoy's share and 25 th of Chandra's share are equal. Find Amar's share.

A
Rs 720
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B
Rs 1080
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C
Rs 450
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D
Rs 1240
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Solution

The correct option is B Rs 1080
According to question,
A6=B4=2C5
Multiplying all three fractions by LCM(6, 4, 5), we get
10A = 15B = 24C
Hence, A+2A3+5A12=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.

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