Question

Rs 4,500 are distributed among x, y and z in such a manner that x receives 3/5 of what y receives, and y receives 1/2 of what z receives. how much does z receive?

Answer 1

X receives 3/5 of Y

X = 3/5 Y

X/Y = 3/5 = 3:5 ....(i)

Y receives 1/2 of Z

Y = 1/2 Z

Y/Z = 1/2 = 1:2 ...(ii)

X:Y = 3:5 ....(from i)

Y:Z = 1:2 .... (from ii)

(ii) multiplied by 5 [to make 'Y' values same]

(ii)== Y:Z = 5:10

X:Y = 3:5

X:Y:Z = 3:5:10

Given total amount = Rs.4500

Z's share = 10/18 * 4500 = 45000/18 = 5000/2 = 2500 Rs.

Answer 2

Given: $x+y+z=4500$ and $x$ receives $\frac{3}{5}y$, $y$ receives $\frac{1}{2}$ of $z$.

$x=\frac{3}{5}y$....(1)

$y=\frac{1}{2}z$....(2)

Using (1) and (2),

$x=\frac{3}{5}\times \frac{1}{2}z$

$x=\frac{3}{10}z$

$x+y+z=4500$

$\frac{3}{10}z+\frac{1}{2}z+z=4500$

$[\frac{6+10+20}{20}]z=4500$

$\frac{36}{20}z=4500$

$z=4500\times \frac{20}{36}$

$z=500\times \frac{20}{4}$

$z=500\times 5$

$z=Rs\ 2500$

Z receives 2500 rupees.

#SPJ2