"> Word Problem 5 | Job Exam Rare Mathematics (JEMrare)

Word Problem 5

Problem 5: Divide Rs 420 among A, B and C so that A may receive 1/2 as much as B and C together and 2/3 of what A and C together receive.

a) 140, 168, 112                         b) 150, 158, 112                          c) 140, 170, 110                 d) 240, 68, 112



Solution:

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 two third of  what A and C get together;

B =\frac{2}{3}(A+C)

————————————-


From 1st condition we can say;

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

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

Sum Of Ratios = 1+2=3

Using share formula;

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

A's Share = \frac{420}{3}\times 1

\Rightarrow A's Share = 140

From 2nd condition we can say;

\frac{B}{A+C}=\frac{2}{3}

Sum Of Ratios=2+3=5

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

 \Rightarrow B's Share=\frac{420}{5}\times 2

 \Rightarrow B's Share= 168

As the amount of Rs 420 is being divided among A, B and C, So, sum of their shares should be equal to 420!

\Rightarrow A+B+C=420 ----(1)

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

\Rightarrow 140+168+C=420

\Rightarrow C=420 -140-168

\Rightarrow C=112

So, the correct option is ‘c’

 

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