Question

A sum of ₹2800 is to be used to award four prizes. If each prize after the first prize is ₹200 less than the preceding prize, find the value of each of the prizes.

Answer 1

Step 1: define the value of each prizes.

Let the first prize be $₹a$.

Second prize =$₹(a-200)$

Third prize = $₹(a-400)$

Fourth prize = $₹(a-600)$

Step 2: compute the value of $a$:

Sum of all prizes is $₹2800$.

$$\begin{gathered} a+\left(a-200\right)+\left(a-400\right)+\left(a-600\right)=2800 \\ \Rightarrow 4a-1200=2800 \\ \Rightarrow 4a=4000 \\ \Rightarrow a=1000 \end{gathered}$$

Therefore, the first prize is $₹1000$.

Step 3: Computing the value of all prizes:

$$\begin{gathered} Secondprize=a-200=800 \\ Thirdprize=a-400=600 \\ Fourthprize=a-600=400 \end{gathered}$$

Hence, the value of each prize is $₹1000,₹800,₹600,\mathrm{and}₹400$.