Rs. 1,875 is divided among A, B, and C in such a way that A’s share is half of the combined share of B and C, and B’s share is one-fourth of the combined share of A and C. By what amount is C’s share more than that of A?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. Rs. 250
Let the shares of A, B and C be a, b, c respectively;
Given:
Total amount = 1875
a + b + c = 1875 Eq 1.
a = (b + c)/2
2a = b + c Eq 2.
b = (a + c)/4
4b = a + c Eq 3.
Putting Eq 2 in Eq 1.
a + b + c = 1875
a + 2a = 1875
a = 625
Put a = 625 in Eq 3.
4b = a + c
4b = 625 + c
4b - 625 = c Eq 4
Put Eq 4 in Eq 1
a + b + c = 1875
625 + b + 4b - 625 = 1875
5b = 1875
b = 375
Now, a + b + c = 1875
625 + 375 + c = 1875
1000 + c = 1875
c = 875.
c - a = 875 = 625 = 250.