Question

The total cost of three prizes is Rs. $2550$. If the value of second prize is ${\left(\frac{3}{4}\right)}^{th}$ of the first prize and the value of $3rd$ prize is $\frac{1}{2}$ of the second prize, then the value of the first prize is ___________.

• A. Rs. $1308$
• B. Rs. $1028$
• C. Rs. $1200$
• D. Rs. $1450$

Answer 1

The correct option is C Rs. $1200$

let the first,second and third prizes be $x,y$ and $z$ respectively

$x+y+z=2550$.....(1)

$y=\frac{3}{4}x$

$z=\frac{1}{2}y=\frac{3}{8}x$

Putting values of $y$ and $z$ in equation (1)

$x+\frac{3}{4}x+\frac{3}{8}x=2550$

$\frac{8x+6x+3x}{8}=2550$

$17x=2550\times 8$

$x=1200$