Rakesh and Rajesh together bought 10 balls and 10 rackets. Rakesh spent ₹ 1300 and Rajesh spent ₹1500. If each racket costs three times a ball does, then what is the price of a racket?

The correct option is ₹210.

Here is the step-by-step explanation to find the price of a racket:

Step 1: Find the total amount spent by Rakesh and Rajesh together.
Rakesh spent ₹1300 and Rajesh spent ₹1500.
Total amount spent = ₹1300 + ₹1500 = ₹2800.

Together, they bought 10 balls and 10 rackets for this total amount of ₹2800.

Step 2: Set up the variables and the equation.
Let the price of one ball be represented by $B$.
Let the price of one racket be represented by $R$.

We are given that each racket costs three times as much as a ball does. Therefore, we can express the price of a racket in terms of the price of a ball as:
$R=3B$

Since they bought 10 balls and 10 rackets, the total cost equation is:
$10B+10R=2800$

Step 3: Substitute the value of $R$ in the equation to find the price of a ball.
Substitute $R=3B$ into the cost equation:
$10B+10\left(3B\right)=2800$
Simplify the equation:
$10B+30B=2800$
$40B=2800$
Divide by 40 to find $B$:
$B=\frac{2800}{40}$
$B=70$
So, the price of a single ball is ₹70.

Step 4: Calculate the price of a racket.
Since a racket costs three times the price of a ball:
$R=3\times 70$
$R=210$
Therefore, the price of a racket is ₹210.