Question

Three prizes are to be distributed in a quiz contest. The value of second prize is ${\frac{5}{6}}^{th}$ of the value of first prize and the value of third prize is ${\frac{4}{5}}^{th}$ of second prize. If the total value of 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 A

Rs. 600, Rs.500, Rs. 400

Let the value of first prize = $x$

Value of second prize = $\frac{5}{6}x$

Value of third prize = $\frac{4}{5}\left(Valueofthesecondprize\right)$
$\Rightarrow \frac{4}{5}\left(\frac{5}{6}x\right)=\frac{2}{3}x$

Total value of three prizes = Rs.1500

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