Question

Three prizes are to be distributed in a quiz contest. The value of the second prize is five-sixth of the value of the first prize and the value of the third prize is four-fifth of the second prize. If the total value of the three prizes is ₹ 1500, then find the value of each prize (in order of 1st, 2nd and 3rd).

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

Answer 1

The correct option is A

₹ 600, ₹ 500, ₹ 400

$\text{Let the value of first prize}=x$

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

$\text{Value of third prize}=\frac{4}{5}\times \text{(Value of the second prize)}=\frac{4}{5}\times \left(\frac{5}{6}x\right)=\frac{4}{6}x=\frac{2}{3}x$

$\text{Total value of three prizes}=₹1500$
$\Rightarrow x+\frac{5}{6}x+\frac{2}{3}x=1500$
$\Rightarrow \frac{6x+5x+4x}{6}=1500$
$\Rightarrow \frac{15x}{6}=1500$
$\Rightarrow 15x=1500\times 6$
$\Rightarrow x=\frac{1500\times 6}{15}$
$\Rightarrow x=600$

$\text{Value of first prize}=₹600$
$\text{Value of second prize}=\frac{5}{6}\times ₹600=₹500$
$\text{Value of third prize}=\frac{2}{3}\times ₹600=₹400$