Question

The average of 13 numbers is 57. The average of first 3 numbers is 48, and that of the next 7 numbers is 58. The 11th number is two times the 12th number and 12th number is 3 less than the 13th number. What is the average of the 11th and 13th numbers ?

• A. 18
• B. 72
• C. 27
• D. 36

Answer 1

Answer:

B. 72

Total of 13 numbers:

$13 \times 57 = 741$

Sum of first 3 numbers

$3 \times 48 = 144$

Sum of next 7 numbers

$7 \times 58 = 406$

Sum of first 10 numbers

$144 + 406 = 550$
Sum of last 3 numbers (11th, 12th, 13th)

$741 - 550 = 191$

Let 12th number = (x)

Then:

• 11th = (2x)

• 13th = (x + 3)

So:
$2x + x + (x + 3) = 191$
$4x + 3 = 191$
$4x = 188 \Rightarrow x = 47$

Find 11th and 13th

• 11th = (2x = 94)

• 13th = (x + 3 = 50)

  Average of 11th and 13th

$\frac{94 + 50}{2} = \frac{144}{2} = 72$

Final Answer: 72