Question

divide rs630 among govind shambhu Ravi and Ganesh so that : govind :shambhu =2:3 shambhu :ravi =4:5 ravi :ganesh =6:7

Answer 1

Govind : Shambhu = 2 : 3 (Given)

Shambhu : Ravi = 4 : 5 (Given)

Ravi : Ganesh = 6 : 7 (Given)

Define x:

Let x be the constant ratio

Govind : Shambhu = 2x : 3x ------------ equation [ 1 ]

Shambhu : Ravi = 4x : 5x ------------ equation [ 2 ]

Ravi : Ganesh = 6x : 7x ------------ equation [ 3 ]

Combine the first two ratios:

[ 1 ] x 4 : Govind : Shambhu = 8x : 12x

[2 ] x 3 : Shambhu : Ravi = 12x : 15x

Now that both Shambhu  has the same ratio in both, we combine them:

Govind : Shambhu : Ravi = 8x : 12x : 15x

Combine the new ratio with the third one:

Govind : Shambhu : Ravi = 8x : 12x : 15x ------------ equation [ 4 ]

Ravi : Ganesh = 6x : 7x ------------ equation [ 3 ]

[ 4 ] x 2 : Govind : Shambhu : Ravi = 16x : 24x : 30x

[3 ] x 5 : Ravi : Ganesh = 30x : 35x

Now that both Ravi has the same ratio in both, we combine them:

Govind : Shambhu : Ravi  : Ganesh = 16x : 24x : 30x  : 35x

Solve x :

16 x + 24x + 30 x + 35x = Rs 630

105x = 630

x = Rs 6

Find their share:

Govind = 16x = 16 (6) = Rs 96

Shambhu= 24x = 24(6) = Rs 144

Ravi  = 30x = 30(6) = Rs 180

Ganesh = 35x = 35 (6) = Rs 210

Answer: Govind  = Rs 96, Shambhu = Rs 144, Ravi  = Rs 180, Ganesh = Rs 210