The income of X and Y …

Let the income of X be Rs. 8x and the income of Y be Rs, 7x.
Further, let the expenditures of x and y be 19y and 16y respectively. Then,
Saving of X = {tex}8x - 19y{/tex}
Saving of Y = {tex}7x - 16y{/tex}
{tex}\therefore{/tex} {tex}8x - 19y = 1250{/tex} .....(i)
and, {tex}7x - 16y = 1250{/tex} .....(ii)
Multiplying equation (i) by 7, and equation (ii) by 8, we get
{tex}56x - 133y = 8750{/tex} ...(iii)
{tex}56x - 128y = 10000{/tex} ....(iv)
Subtracting equation (iv) from equation (iii), we get
{tex}-133y + 128y = 8750 - 10000{/tex}
{tex}\Rightarrow{/tex} {tex}-5y = -1250{/tex}
{tex}\Rightarrow y = \frac{{ - 1250}}{{ - 5}} = 250{/tex}
Putting y = 250 in equation (i), we get
{tex}8x - 19\times 250 = 1250{/tex}
{tex}\Rightarrow{/tex} {tex}8x - 4750 = 1250{/tex}
{tex}\Rightarrow{/tex} {tex}8x = 1250 + 4750{/tex}
{tex}\Rightarrow x = \frac{{6000}}{8} = 750{/tex}
Thus, X's income = 8x = 8 {tex}\times{/tex} 750 = Rs.6000
Y's income = 7x = 7 {tex}\times{/tex} 750 = Rs.5250.