Question

A sum of ` 3700 is divided among A, B and C such that B’s share is thrice of A’s share and

C’s share is ` 200 more than B’s share. Find the share of A.​

Answer 1

The share of A is Rs. 500.

Step-by-step-explanation:

We have given that,

A sum of 3700 is divided among A, B and C.

∴ Sum of shares of A, B and C = 3700

⇒ A + B + C = 3700

⇒ A = 3700 - B - C - - - ( 1 )

From the first condition,

B's share = 3 * A's share

⇒ B = 3A

⇒ B = 3 * ( 3700 - B - C )

⇒ B = 11100 - 3B - 3C

⇒ B + 3B = 11100 - 3C

⇒ 4B = 11100 - 3C - - - ( 2 )

From the second condition,

C's share = B'share + 200

⇒ C = B + 200

By using this value in equation ( 2 ), we get,

4B = 11100 - 3C - - - ( 2 )

⇒ 4B = 11100 - 3 ( B + 200 )

⇒ 4B = 11100 - 3B - 600

⇒ 4B + 3B = 11100 - 600

⇒ 7B = 10500

⇒ B = 10500 ÷ 7

⇒ B = 1500

⇒ B's share = 1500 Rs.

Now, by using this value in equation ( 1 ),

A = 3700 - B - C - - - ( 1 )

⇒ A = 3700 - 1500 - ( B + 200 )

⇒ A = 3700 - 1500 - ( 1500 + 200 )

⇒ A = 2200 - 1700

⇒ A = 500

⇒ A's share = 500 Rs.

∴ The share of A is Rs. 500.✅