Question
Rs. 5625 is divided among A, B and C so that A receives
one half as much as B and C together receive and B receives one-fourth of what A and C together receive. The share of A is more than that of B by:Solution
Total = Rs. 5625
A = (1/2}) x (B + C)
B = (1/4}) x (A + C)
Let B = x
A + C = 4 x ⇒C = 4x – A …(1)
A = 1/2 (B + C) = 1/2 (x + C) ⇒ 2A = x + C ….(2)
Substitute C from (1) into (2):
2A = x + (4x − A) ⇒ 2A = 5x – A
⇒ 3A = 5x ⇒A = 5x/3
Now, C = 4x – A = 4x − 5x/3 = (12x − 5x)/3 = 7x/3
A + B + C = (5x/3) + x + (7x/3) = 15x/3 =5x
5x = 5625 ⇒x = 1125
A = 5x/3 = (5 × 1125)/3 =1875
A – B = 1875 – 1125 = 750
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