Average of three numbers is 22. Sum of two of the numbers is 24 and these two…
2020
Average of three numbers is 22. Sum of two of the numbers is 24 and these two numbers are in the ratio 7 : 5. Find the three numbers.
- A.
-6, 30, 42
- B.
6, 25, 35
- C.
14, 10, 42
- D.
4, 20, 42
Attempted by 10 students.
Show answer & explanation
Correct answer: C
Concept: For n numbers, Average = (Sum of the numbers) ÷ n, so Sum = Average × n. When two of those numbers are in a ratio a : b, write them as ax and bx and use their given sum to find x.
The average of the three numbers is 22, so their total sum = 22 × 3 = 66.
The two numbers that are in the ratio 7 : 5 add up to 24. Writing them as 7x and 5x gives 7x + 5x = 24, so 12x = 24 and x = 2.
This gives the two ratio numbers as 7x = 14 and 5x = 10.
The third number = Total sum − 24 = 66 − 24 = 42.
Cross-check: 14 + 10 + 42 = 66, and 66 ÷ 3 = 22 — this matches the given average.
So the three numbers are 14, 10 and 42.