Question

The total cost of three prizes is Rs. 2550. If the value of second prize is $\frac{3}{4}$th of the first and the value of 3rd prize is $\frac{1}{2}$ of the second prize;
find the value of first prize.

• A. Rs. $900$
• B. Rs. $1500$
• C. Rs. $1200$
• D. Rs. $450$

Answer 1

The correct option is C Rs. $1200$

Let First Prize be $x$
Then Second Prize $=\frac{3}{4}x$

Third Prize $=\frac{1}{2}\times \frac{3x}{4}=\frac{3x}{8}$

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

L.C.M of $1,4,8$ is $8$.

$\frac{x\times 8}{1\times 8}+\frac{3x\times 2}{4\times 2}+\frac{3x}{8}=2550$
$\frac{8x+6x+x}{8}=2550$

$\frac{17x}{8}=2550$

$x=\frac{2550\times 8}{17}$

$x=Rs.1200$

$\therefore$ The value of first first prize is $Rs.1200$