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?

Correct Option (C)

Let the cost of one ball be Rs. x and the cost of one racket be Rs. 3x, as per the condition that each racket costs three times a ball. The total number of balls purchased is 10, and the total number of rackets purchased is 10. The combined expenditure by Rakesh and Rajesh is Rs. (1300 + 1500) = Rs. 2800. The total expenditure can be represented by the equation:

10(x) + 10(3x) = 2800
10x + 30x = 2800
40x = 2800
x = $\frac{2800}{40}=70$

This value x = 70 signifies the price of one ball. The price of one racket is 3x. Therefore, the price of a racket = 3 × 70 = Rs. 210.

Incorrect Options:

Options A (Rs. 70), B (Rs. 90), and D (Rs. 240) are incorrect. The calculated price of a racket, based on the total expenditure of Rs. 2800 for 10 balls and 10 rackets, and the specified cost relationship where a racket costs three times a ball, is Rs. 210. These alternative options do not satisfy the given conditions and the derived algebraic solution.