Question

An amount of 5600 is divided among A, B and C. A gets three-fourth of the total amount received by B and C. C gets one-sixth of the total amount received by A and B. Find the amount received by B.​

Answer 1

Step-by-step explanation:

Sum = Rs 5600

The sum of the share of B and C is equal to thrice the share of A

B+C = 3A

B = 3A - C

The sum of the share of B and C is equal to nine-fifths the share of B

A+C = 9/5B

5A+5C = 9B

Find the ratio of C: A

B = 3A-C

5A+5C = 9B

Sub 1 into 2

5A + 5C = 9( 3A-C)

5A + 5C = 27A-9C

14C = 22A

7C = 11A

C:A = 11 : 7

Find the ratio of B:C

7C = 11A

B = 3A-C

Sub 3 into 1

B + C = 3(7/11C

11B + 11C = 21C

11B = 10C

B : C = 10 : 11

Find the ratio of A : B : C

C : A = 11 : 7

B : C = 10 : 11

C : A : B = 11 : 7 :10

A : B : C = 7 : 10 : 11

7x + 10x + 11x = 5600

28x = 5600

x = 5600 ÷ 28

x = 200

7x = 7 × 200 = 1400

10x = 10 × 200 = 2000

11x = 11 × 200 = 2200

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