Question

A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following results are obtained: 
(i) The sum of Yellow balls and twice the number of Violet balls is 50. 
(ii) The sum of Violet and Green balls is 50. 
(iii) The sum of Yellow and Red balls is 50. 
(iv) The sum of Violet and twice the number of Red balls is 50.

• A.
• B.
• C.
• D.

Hint:

Assume the total is 100 when pie chart percentages are given. Translate each condition into equations and verify using actual values from the options.

Answer 1

The Correct Option is A

Let the total number of balls be 100 (since percentages are given). So, the actual number of each type of ball in option (A) is: \[ V = 10, \quad Y = 30, \quad R = 20, \quad G = 40 \]
Now verify the conditions:

(i) \( Y + 2V = 30 + 2 \times 10 = 30 + 20 = 50 \) ✔️
(ii) \( V + G = 10 + 40 = 50 \) ✔️
(iii) \( Y + R = 30 + 20 = 50 \) ✔️
(iv) \( V + 2R = 10 + 2 \times 20 = 10 + 40 = 50 \) ✔️

All conditions are satisfied only in option (A). Other options do not verify all four conditions simultaneously.