Question
Download Solution PDFAverage of 4 numbers is 45. Average of first two numbers is thrice the average of other two numbers. What is the sum of first two numbers?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The average of four numbers is 45
The average of the first two numbers is thrice the average of the other two numbers
Concept used:
Average × Number of entities = Total
Calculation:
Let the first two numbers be a and b and the last two be c and d.
⇒ (a + b)/2 = 3 × (c + d)/2
⇒ (a + b) = 3 × (c + d)
⇒ a + b + c + d = 4 × 45 = 180
⇒ a + b + (a + b)/3 = 180
⇒ a + b (1 + 1/3) = 180
⇒ a + b × 4/3 = 180
⇒ a + b = 135
∴ The answer is 135.
Shortcut Trick
Let the average of the last two numbers be 1 unit.
Then the average of the first two numbers = 1 × 3 = 3 units
The sum of the first two = 2 × 3 = 6 units
⇒ 1 × 2 + 2 × 3 = 4 × 45
⇒ 8 units = 180
⇒ 6 units = 180 × 6/8 = 135
Last updated on Jul 14, 2025
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