Question

A total of 700 is divided among A, B and C such that the money
received by A and B is in the ratio 2:3 and the money received by C and
B is in the ratio 5:4. Find the amount received by each of them,

Answer 1

Answer:

answer is 233.30

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Answer 2

Total amount of money divided among A, B, C = Rs. 700

Writing the above statement in the form of equation using variables and constants :

⇒ A + B + C = 700 → Equation ( 1 )

Ratio of money received by A and B = 2 : 3

Writing the above statement in the form of equation using variables and constants :

⇒ A / B = 2 / 3

⇒ 3A = 2B

⇒ A = 2B / 3 → Equation ( 2 )

Ratio of money received by C and B = 5 : 4

Writing the above statement in the form of equation using variables and constants :

⇒ C / B = 5 / 4

⇒ C = 5B / 4 → Equation ( 3 )

Substituting Equation ( 2 ) and Equation ( 3 ) in Equation ( 1 ) such that we can express all 3 variables A, B and C in terms of B

⇒ A + B + C = 700

⇒ 2B/3 + B + 5B/4 = 700

To add the unlike fractions in LHS make all denominators equal by taking LCM of denominators [  LCM( 3, 1, 4 ) = 12 ]

⇒ ( 8B + 12B + 15B ) / 12 = 700

⇒ 5B / 12 = 100

⇒ 5B = 1200

⇒ B = 1200/5

⇒ B = 240

∴ amount received by B is Rs. 240

Now calculate the amount received by A by substituting the value of B in Equation ( 2 )

⇒ A = 2B / 3

⇒ A = 2( 240 ) / 3

⇒ A = 160

∴ amount received by A is Rs. 160

Now calculate the amount received by C by substituting the value of B and A in Equation ( 1 )

⇒ 160 + 240 + C = 700

⇒ 400 + C = 700

⇒ C = 700 - 400

⇒ C = 300

∴ amount received by C is Rs. 300