Question

atul, bheem and chandan played a game. in the first round atul lost the game and he gave bheem and chandan whatever money they had. in the second round bheem lost the game and he gave atul and chandan whatever money they had. in the third round chandan lost the game and he gave atul and bheem whatever money they had. at the end they found that they had an equal amount of rs. 160 with them. what was the initial amount with chandan?

Answer 1

Answer:

₹160

Step-by-step explanation:

because money are revolving to there friend at end they got equal money

Answer 2

• The initial amount with chandan was equal to Rs. 80 .

Given :-

• Atul, Bheem and Chandan played a game.
• First round :- Atul lost and gave bheem and chandan whatever money they had .
• Second round :- Bheem lost and gave atul and chandan whatever money they had .
• Third round :- Chandan lost and gave atul and bheem whatever money they had .
• At the end they had an equal amount of Rs. 160 .

To Find :-

• What was the initial amount with chandan ?

Solution :-

Let us assume that,

• The initial amount with Atul has Rs. A .
• The initial amount with Bheem has Rs. B .
• The initial amount with Chandan has Rs. C .

Case 1) :- Atul lost

→ Atul gave to bheem = Rs. B

→ Atul gave to chandan = Rs. C

So,

→ Left amount to atul = Rs. (A - B - C)

→ Bheem new amount = B + B = Rs. 2B

→ Chandan new amount = C + C = Rs. 2C

Case 2) :- Bheem lost

→ Bheem gave to atul = Rs. (A - B - C)

→ Bheem gave to chandan = Rs. 2C

So,

→ Left amount to bheem = 2B - (A - B - C + 2C) = Rs. (3B - A - C)

→ Atul new amount = Rs. 2(A - B - C)

→ Chandan new amount = 2 × 2C = Rs. 4C

Case 3) :- Chandan lost

→ Chandan gave to atul = Rs. 2(A - B - C)

→ Chandan gave to bheem = Rs. (3B - A - C)

So,

→ Left amount to Chandan = 4C - 2(A - B - C) - (3B - A - C) = 4C - (2A - 2B - 2C + 3B - A - C) = Rs. (7C - A - B)

→ Atul new amount = Rs. 4(A - B - C)

→ Chandan new amount = Rs. 2(3B - A - C)

A/q,

→ Left amount to chandan = Atul new amount = Chandan new amount = Rs. 160

So,

→ 7C - A - B = 160 -------- Equation (1)

→ 4(A - B - C) = 160

→ A - B - C = 40 --------- Equation (2)

→ 2(3B - A - C) = 160

→ 3B - A - C = 80 ---------- Equation (3)

Adding Equation (1) and Equation (2) we get,

→ (7C - A - B) + (A - B - C) = 160 + 40

→ 6C - 2B = 200

→ 2(3C - B) = 200

→ 3C - B = 100

→ B = (3C - 100) --------- Equation (4)

putting Equation (4) in Equation (2) now,

→ A - (3C - 100) - C = 40

→ A - 3C + 100 - C = 40

→ A - 4C = 40 - 100

→ A = (4C - 60) ------- Equation (5)

Putting Equation (4) and Equation (5) in Equation (3) now,

→ 3(3C - 100) - (4C - 60) - C = 80

→ 9C - 300 - 4C + 60 - C = 80

→ 4C - 240 = 80

→ 4C = 80 + 240

→ 4C = 320

→ C = Rs. 80 (Ans.)

Hence, the initial amount with chandan was equal to Rs. 80 .

Extra :- The initial amount with Atul was Rs. 260 and the initial amount with Bheem was 140 .

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