The average of three numbers is 180. If the third number is greater by 10 than 1/3 of the first number and less by 5 than the second number, then the third number is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 113.
Formula used:
Average = Sum of observations/number of observations ---- (1)
Calculations:
Let the three numbers be a, b and c
Using equation (1)
a + b + c = 180 × 3 = 540 ---- (1)
⇒ c - a/3 = 10
⇒ a - 3c = -30 ---- (2)
and b - c = 5 ---- (3)
Subtract equation (3) from (1), we get
⇒ a + 2c = 535 ----- (4)
Subtract equation (2) from (4), we get
⇒ a + 2c + 3c - a = 535 + 30
⇒ 5c = 565
⇒ c = 113