Question

The average of 13 numbers is 70. The average of the first five numbers is 60. The average of the next five numbers is 25 % higher than the average of the first five numbers. The 11th number is 6 less than the 13th number, and the 12th number is 4 greater than the 13th number. What is the average of the 11th and 12th numbers?

• A. 78
• B. 77
• C. 76
• D. 74

Answer 1

Answer:

A. 78

Average of 13 numbers (=70)

So, total sum of 13 numbers:

$13 \times 70 = 910$

First 5 numbers

Average (=60)

Sum:

$5 \times 60 = 300$

Next 5 numbers

Average is (25%) higher than 60:

$60 + 25\% \text{ of } 60 = 60+15=75$

Sum of next 5 numbers:

$5 \times 75 = 375$

So, sum of first 10 numbers:

$300+375=675$

Therefore, sum of 11th, 12th, and 13th numbers:

$910-675=235$

Let the 13th number be (x).

Then:

• 11th number (= x-6)

• 12th number (= x+4)

So,

$(x-6)+(x+4)+x=235$

$3x-2=235$
$3x=237$
$x=79$

Thus,

• 11th number (=73)

• 12th number (=83)

Average of 11th and 12th numbers:

$\frac{73+83}{2}=\frac{156}{2}=78$
$\boxed{78}$