Question

Divide ₹760 among A B C such that A gets 5/6 of what B gets and the ratio between the shares of B and C is 3:4

Answer 1

Let us X, Y, and Z are amounts in 760 that A, B, and C get.

X = 5Y / 6  --- equation  1

Given, Y : Z = 3 : 4  or,  Y/Z = 3/4      or   Y = 3Z/4

         substitute in equation 1
     X = 5/6 * 3/4 * Z  = 5Z/8

Add X, Y, and Z,         5Z/8 + 3Z/4 + Z  = 760

Z [ 5/8 + 3/4 + 1 ] = 760
Z ( 5+3*2+8)/8  = 760

Z * 19/8  = 760

Z = 760 * 8/19 = 320

Y = 3Z/4 = 240

X = 5Y/6 = 200

Answer 2

let amount of B = x 
then amount of A = 5x/6
and ratio of B/C=3/4
          so, x/C = 3/4
        therefore amount of C = 4x/3
A/Q,     
          A+B+C = 760
$or, \frac{5x}{6} +x+ \frac{4x}{3} = 760$
$or, \frac{19x}{6} =760$
$or, x = \frac{760*6}{19} =240$
therefore amounts of A = 5*240/6 = 200 rupees
                               B = 240 rupees
                               C = 320 rupees