Question

Three prizes are to be distributed in a quiz contest. The value of the second prize is $\frac{5}{6}$ of the value of the first prize and the value of the third prize is $\frac{4}{5}$ of the second prize. If the total value of the three prizes is Rs.1500. Find the value of each prize. (in order of 1^st, 2^nd & 3^rd)

• A. Rs. 600, Rs.500, Rs. 400
• B. Rs.500, Rs. 400, Rs.600
• C. Rs.900, Rs.400, Rs.300
• D. Rs.700, Rs.500, Rs.300

Answer 1

The correct option is

B

Rs. 600, Rs.500, Rs. 400

Let the value of first prize = $x$

Value of second prize = $\frac{5}{6}$(value of the first prize)$=\frac{5}{6}x$

Value of third prize = $\frac{4}{5}$ (Value of the second prize)

= $\frac{4}{5}$ ($\frac{5}{6}x$) = $\frac{2}{3}x$

Total value of three prizes $=Rs.1500$

$\Rightarrow x+\frac{5}{6}x+\frac{2}{3}x=1500$
$\Rightarrow$ $\frac{6x+5x+4x}{6}=1500$
$\Rightarrow$ $\frac{15x}{6}=1500$
$\Rightarrow x=600$
Hence, Value of first prize $=Rs.600$
Value of second prize = $\frac{5}{6}$ $\times$ $Rs.600=Rs.500$
Value of third prize = $\frac{2}{3}$ $\times$ $Rs.600=Rs.400$