Question

Rs. 2250 is divided among three boys named rama, krishna and kalki in such a way that 1/6th of rama's share, 1/4th of krishna's share and 2/5th of kalki's share are equal. find rama's share.

Answer 1

Let rama's share be r, Krishna's share be k and Kalki's share be l.

rama's share will be :

2250 - (k + l)

1/6r = 1/4k = 2/5l

1/6r = 1/6(2250 - k - l)

= 375 - 1/6k - 1/6l

375 - 1/6k - 1/6l = 1/4 k

375 - 1/6k - 1/4k - 1/6l = 0

-5/12k - 1/6l = - 375

5/12k + 1/6l = 375

30k + 12l = 27000..... 1

375 - 1/6k - 1/6l = 2/5l

375 - 1/6 k - 17/30l = 0

1/6k + 17/30l = 375

30k + 102l = 67500........ 2

Solving 1 and 2 simultaneously :

90l = 40500

l = 450

30 k + 12 × 450 = 27000

30k = 21600

K = 21600/30

K = 720

Rama's share :

2250 - (720 + 450) = 1080