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Word Problem 4 (Share calculation as per condition)

Problem 4: Divide Rs 5625 among A, B and C so that A may receive 1/2 as much as B and C together, and B 1/4th of what A and C together receive.

a) 1125, 1875, 2630                b) 1875, 1125, 2625             c) 2625, 1875, 1125                     d) none



Solution:

(general math for jobs)

Here,

1st Condition:

A receives half of what  B and C get together;

i-e

A = \frac{1}{2}(B+C)

2nd Condition

B receives one fourth of what A and C receive together;

i-e

B = \frac{1}{4}(A+C)

———————————————————————–

From 1st condition we can write;

\frac{A}{B+C}=\frac{1}{2}

\Rightarrow A : (B+C)=1:2

\Rightarrow Sum Of Ratios=1+2=3

Using share formula;

A's Share=\frac{Total Amount}{Sum Of Ratio}\times A's Ratio

\Rightarrow A's Share=\frac{5625}{3}\times 1

\Rightarrow A's Share= 1875

In the same way from 2nd condition we can write;

 \frac{B}{A+C}=\frac{1}{4}

\Rightarrow B: (A+C)=1:4

\Rightarrow Sum Of Ratios=1+4=5

Using formula of share calculation;

B's Share=\frac{Total Amount}{Sum Of Ratio}\times B's Ratio

B's Share=\frac{5625}{5}\times 1

B's Share=1125

Also we know that total amount is being divided among A, B and C, so sum of their shares should be 5625!

\Rightarrow A+B+C = 5625 ----(1)

Put values of A’s share and B’s share in eq (1)

\Rightarrow 1875+1125+C = 5625

\Rightarrow C=5625-1875-1125=2625

So, we have calculated shares of A,B and C

So option  ‘b’ is the answer

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