Akbar, Birbal, Chaitanya, David & Ehsaan play a game of coins. Akbar says to…

2025

Akbar, Birbal, Chaitanya, David & Ehsaan play a game of coins. Akbar says to Birbal, "If you give me 30 coins, you will have as many as Ehsaan has, and if I give you 30 coins, you will have as many as David has." Akbar and Birbal together have 100 coins more than what David and Ehsaan together have. If Birbal has 20 coins more than what Chaitanya has, and the total number of coins that they have is 1330, how many coins does Birbal have?

  1. A.

    220

  2. B.

    230

  3. C.

    250

  4. D.

    350

Show answer & explanation

Correct answer: C

A word problem that describes several linked unknown quantities — coin counts, ages, amounts — can always be modelled as a SYSTEM OF LINEAR EQUATIONS: assign one variable per unknown, translate each stated relationship into an equation connecting those variables, and then use substitution to collapse the system into a single equation in the one unknown the question asks for.

  1. Let Akbar, Birbal, Chaitanya, David and Ehsaan's coin counts be A, B, C, D and E respectively.

  2. "If you (Birbal) give me 30 coins, you will have as many as Ehsaan has" translates to B − 30 = E.

  3. "If I (Akbar) give you 30 coins, you will have as many as David has" translates to B + 30 = D.

  4. Adding these two relations: D + E = (B + 30) + (B − 30) = 2B.

  5. "Akbar and Birbal together have 100 coins more than David and Ehsaan together" translates to A + B = D + E + 100 = 2B + 100, so A = B + 100.

  6. "Birbal has 20 coins more than Chaitanya" translates to B = C + 20, so C = B − 20.

  7. The total-coins condition gives A + B + C + D + E = 1330.

  8. Substituting every relationship in terms of B: (B + 100) + B + (B − 20) + 2B = 1330, which simplifies to 5B + 80 = 1330, so 5B = 1250 and B = 250.

Check: with B = 250, E = 220, D = 280, A = 350 and C = 230. The five totals check out — A + B + C + D + E = 350 + 250 + 230 + 280 + 220 = 1330; A + B = 600 is exactly 100 more than D + E = 500; B − 30 = 220 = E; B + 30 = 280 = D; and C + 20 = 250 = B — every stated condition holds, confirming Birbal has 250 coins.

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