Answer : Option D
Explanation :
ATQ,
A: B = 1: 2........... (i)
B: C = 3: 1........... (ii)
C: D = 2: 3...........(iii)
Now,
Find A: B: C: D
Step 1: A: B: C: D
1: 2 (A: B value by equation i)
Note: To understand the shortcut, remember you need to make the right-hand side missing numbers the same as that of last given number, and for the right-hand side the same is done.
i.e., C: D will contain 2: 2 because 2 is the last number on the right side.
Or, A: B: C: D
1: 2: 2: 2
3: 3: 1: 1 (B: C value by equation ii)
2: 2: 2: 3 (C: D value by equation iii)
Now, multiply vertically and to get A: B: C: D.
So, A: B: C: D = (1*3*2): (2*3*2): (2*1*2): (2*1*3)
= 6: 12: 4: 6
= 3: 6: 2: 3
Now, the share of A and C = [(A+C)/ (A+B+C+D)] * total amount
Or, the share of A and C = [(3+2)/ (3+6+2+3)] * 5600
Or the share of A and C = (5/14)*5600 = 2000
Similarly, the share of B and C = (8/14)*5600 = 3200
Solution 2:
Find A: B: C: D
1: 2: 2: 2
3: 3: 1: 1
2: 2: 2: 3
Now, multiply vertically and get A: B: C: D.
So, A: B: C: D = (1*3*2): (2*3*2): (2*1*2): (2*1*3)
Or, A: B: C: D = 6: 12: 4: 6
Or, A: B: C: D = 3: 6: 2: 3
Sum of the ratios = 3+6+2+3 = 14, but ATQ, it is 5600 Rs.
i.e., 14 * 400 = 5600
So, multiply each and every ratio by 400 and get the share of each:
3*400: 6*400: 2*400: 3*400
So, the share of A = 1200
The share of B = 2400
The share of C = 800
The share of D = 1200
Now, the share of (A+C) = 1200+800 = 2000
The share of (B+C) = 2400+ 800 = 3200
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