Question

Divide Rs. 500 between Arham, Mariam and Sarim so that Arham gets 2/3 of what Mariam gets and Mariam gets 1/4 of what Sarim gets. Find the share of each.

Answer 1

Let the share of Arham be "x" 
share of Mariam be "y"
and share of Sarim be "z"
Given that, Arham gets 2/3 of what Mariam gets,
therefore, x = (2/3).y  .......... (1)
Also given that, Mariam gets 1/4 of what Sarim gets,
therefore, z = (1/4). (x+y)  ........ (2)
Total amount is Rs. 500
Hence, x + y + z = 500   ......... (3)
Now put the values of x and z in equation 3, we get:
2y/3 + y + x/4 + y/4 = 500
(8y + 12y + 3x + 3y) /12 = 500
(23y + 3x) / 12 = 500
 [23y + 3 (2y/3) ] / 12 = 500
(23y + 2y) / 12 = 500
25y / 12 = 500
y = (500/25).12
y = 20 x 12
y = 240
Now put this value in equation (1), we get:
x = (2/3). 240
x = 160
Now put these values in equation (3), we get:
160 + 240 + z = 500
400 + z = 500
z = 500 - 400
z = 100
which shows that Arham gets Rs. 160, Mariam gets Rs. 240 and Sarim gets Rs. 100.

Answer 2

Solution :-

Let the share of Sarim be Rs.'x'

Given - Mariam gets 1/4th of what Sarim gets.

⇒ x*1/4

⇒ Mariam gets x/4

Also given that Arham gets 2/3 what Mariam gets.

⇒ 2/3 of x/4

⇒ 2/3*x/4

⇒ 2x/12

⇒ Arham gets x/6 

Now, according to the question.

⇒ x/1 + x/4 + x/6 = 500

Taking LCM of the denominators and then solving it.

⇒ (12x + 3x + 2x)/12 = 500

⇒ 17x = 12*500

⇒ x = 6000/17

⇒ x = 352.94 or Rs. 353 (Approximately)

So, share of Sarim is Rs. 353

Now, share of Mariam = 353/4 

Share of Mariam = Rs. 88.25 or Rs. 88 (Approximately)

Now, share of Arham = (2*88)/3

Share of Arham = Rs. 58.66 or Rs. 59 (Approximately)

So, Sarim gets Rs. 353, Mariam gets Rs. 88 and Arham gets Rs. 59 respectively.

Answer.