Question

Three prizes are to be distributed in a quiz contest. The value of the second prize is one-fifth of the value of the first prize and the value of the third prize is two-third of the second prize. If the total value of the three prizes is ₹ 2000, then find the value of each prize (in order of 1st, 2nd and 3rd).

• A. ₹ 900, ₹ 600, ₹ 500
• B. ₹ 1000, ₹ 500, ₹ 400
• C. ₹ 1500, ₹ 300, ₹ 200
• D. ₹ 1700, ₹ 200, ₹ 100

Answer 1

The correct option is C ₹ 1500, ₹ 300, ₹ 200

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

$\text{Value of second prize}=\frac{1}{5}x$

$\text{Value of third prize}=\frac{2}{3}\times \text{(Value of the second prize)}=\frac{2}{3}\times \left(\frac{1}{5}x\right)=\frac{2}{15}x$

$\text{Total value of three prizes}=₹2000$
$\Rightarrow x+\frac{1}{5}x+\frac{2}{15}x=2000$
$\Rightarrow \frac{15x+3x+2x}{15}=2000$
$\Rightarrow \frac{20x}{15}=2000$
$\Rightarrow 20x=2000\times 15$
$\Rightarrow x=\frac{2000\times 15}{20}$
$\Rightarrow x=1500$

$\text{Value of first prize}=₹1500$
$\text{Value of second prize}=\frac{1}{5}\times ₹1500=₹300$
$\text{Value of third prize}=\frac{2}{3}\times ₹300=₹200$