The average of 12 numbers is 52. The average of the first 4 numbers is 42 and the average of the next 5 numbers is 56. If the 10th number is 7 less than 11th number and the 12th number is 3 less than the 11th number, then what is the average of the 10th and 12th number?
The average of 12 numbers is 52. The average of the first 4 numbers is 42 and the average of the next 5 numbers is 56. If the 10th number is 7 less than 11th number and the 12th number is 3 less than the 11th number, then what is the average of the 10th and 12th number? Correct Answer 57
Solution :
Given data :
The average of 12 numbers = 52
The average of first 4 numbers = 42
The average of next 5 numbers = 56
Concept used :
Average = (Sum of all units)/(Number of all units)
Calculation :
Assume, 11th number be x
⇒ 10th number = x – 7
⇒ 12th number = x – 3
Sum of 12 numbers = 12 × 52
⇒ 624
Sum of First 4 numbers = 4 × 42
⇒ 168
Sum of next 5 numbers = 5 × 56
⇒ 280
Sum of all numbers = 168 + 280 + x + (x – 7) + (x – 3)
⇒ 448 + 3x – 10 = 624
⇒ 438 + 3x = 624
⇒ 3x = 624 – 438
⇒ 3x = 186
⇒ x = 186/3
⇒ x = 62
⇒ 10th number = x – 7
⇒ 62 – 7
⇒ 55
⇒ 11th number = x
⇒ 62
⇒ 12th number = x – 3
⇒ 62 – 3
⇒ 59
Average number of 10th and 12th number = (55 + 59)/2
⇒ 114/2
⇒ 57
∴ The average of 10th and 12th number is 57.
Alternate method :
⇒ 10th number = x – 7
⇒ 62 – 7
⇒ 55
⇒ 11th number = x
⇒ 62
⇒ 12th number = x – 3
⇒ 62 – 3
⇒ 59
Average number of 10th and 12th number = (55 + 59)/2
⇒ 114/2
⇒ 57
∴ The average of 10th and 12th number is 57.
