Question

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

Answer 1

Answer

Let the cost distributed to first friend be y

Let the cost distributed to second friend be 2y

Let the cost distributed to third friend be $\sf \dfrac{1}{2} (y + 2y)$

Money distributed to first friend :

According to the question,

$\sf \dashrightarrow y : 2y : \dfrac{1}{2} (y + 2y) = 9000$

$\sf \dashrightarrow y + 2y + \dfrac{1}{2} (y + 2y) = 9000$

$\sf \dashrightarrow 3y + \dfrac{1}{2} (y + 2y) = 9000$

$\sf \dashrightarrow 3y + \dfrac{1}{2} (3y) = 9000$

$\sf \dashrightarrow 3y + \dfrac{3y}{2} = 9000$

$\sf \dashrightarrow \dfrac{6y + 3y}{2} = 9000$

$\sf \dashrightarrow \dfrac{9y}{2} = 9000$

$\sf \dashrightarrow 9y = 9000 \times 2$

$\sf \dashrightarrow 9y = 18000$

$\sf \dashrightarrow y = \dfrac{18000}{9}$

$\sf \dashrightarrow y = 2000$

Now, we can find the money distributed to second and third friend.

Money distributed to second friend :

$\sf \dashrightarrow 2y = 2(2000)$

$\sf \dashrightarrow Rs.4000$

Money distributed to third friend :

$\sf \dashrightarrow \dfrac{1}{2} (y + 2y)$

$\sf \dashrightarrow \dfrac{1}{2} (2000 + 4000)$

$\sf \dashrightarrow \dfrac{1}{2} (6000)$

$\sf \dashrightarrow \dfrac{6000}{2}$

$\sf \dashrightarrow Rs.3000$

Hence, the money distributed to first, second and third friends are ₹2000, ₹4000 and ₹3000 respectively.