There are total 24 hats of blue and red colour. The average cost of blue colour hats is Rs. 65. The average cost of red colour hats is Rs. 35. The average cost of all the hats is Rs. 50. What is the number of red colour hats?
Show answer & explanation
Correct answer: A
Explanation
Given:
Total number of caps = 24
Average value of blue caps = 65
Average value of red caps = 35
Overall average = 50
According to the formula:
Total value = (Number of blue caps × Average value of blue caps) + (Number of red caps × Average value of red caps)
Total number of caps = Number of blue caps + Number of red caps
Let the number of red caps = x
Number of blue caps = 24 − x
Overall average = [(24 − x) × 65 + x × 35] / 24 = 50
⇒ (1560 − 65x + 35x) / 24 = 50
⇒ (1560 − 30x) / 24 = 50
⇒ 1560 − 30x = 1200
⇒ 30x = 360
⇒ x = 12