Question

Rupees 9000 is distributed among 3 friends in such a manner that the second friend gets twice
the amount of the first friend and the third friend gets exactly the half of the total amount of the
first two friends. Calculate how much money each of them will get.​

Answer 1

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Answer 2

Given :-

Total amount = Rs. 9000

Amount for second friend = 2 × Amount of first friend

Amount for third friend = Half of the total amount of the  first two friends.

To Find :-

Total amount of first friend.

Total amount of second friend.

Total amount of third friend.

Solution :-

Let first friend get Rs. x

Second friend = Rs, y

Third friend = Rs. z

By first case,

$\sf x+y+z=9000 \qquad ...(1)$

By second case,

$\sf y=2y \qquad ...(2)$

By third case,

$\sf z=\dfrac{(x+y)}{2} \qquad ...(3)$

Substituting (2) in (3),

$\sf z=\dfrac{(x+2x)}{2}$

$\sf z=\dfrac{3x}{2} \qquad ...(4)$

Substituting (2), (4) in (1),

$\sf x+2x+\dfrac{3x}{2} =9000$

$\sf 3x+\dfrac{3x}{2} =9000$

$\sf 3 \bigg( x+\dfrac{x}{2} \bigg)=9000$

$\sf x+\dfrac{x}{2} =3000$

$\sf \dfrac{3x}{2} =3000$

$\sf 3x=6000$

$\sf x=2000 \qquad ...(5)$

∴ Amount for first friend = x = Rs. 2000

Substituting (5) in (2),

$\sf y=2 \times 2000$

$\sf y=Rs. \ 4000$

∴ Amount for second friend = Rs. 4000

Substituting (5) in (4),

$\sf z=\dfrac{3 \times 2000}{2} =Rs. \ 3000$

∴ Amount for third friend = Rs. 3000