The average of twelve numbers is 39. The average of the last five numb

1.	The average of twelve numbers is 39. The average of the last five numbers is 35, and that of the first four numbers is 40. The fifth number is 6 less than the sixth number and 5 more than the seventh number. The average of the fifth and sixth numbers is:1. 442. 473. 504. 39
Answer» Correct Answer - Option 2 : 47 Given: The average of twelve numbers = 39. The average of the last five numbers = 35, The average of the first four numbers = 40. The fifth number is 6 less than the sixth number and 5 more than the seventh number. Concept Used: Sum = Average × total number Solution: The Sum of the twelve numbers = 12 × 39 = 468 The sum of the last five number = 5 × 35 = 175 The sum of the first four number = 4 × 40 = 160 The sum of the fifth, sixth and seventh number = (468 – 175 – 160) = 133 Let, the fifth number is x Then, the sixth number is (x + 6) and the seventh number is (x – 5) x + (x + 6) + (x – 5) = 133 ⇒ 3x + 1 = 133 ⇒ 3x = 132 ⇒ x = 44 The fifth number is 44 and the sixth number is (44 + 6) = 50 Average of fifth and sixth number is (44 + 50)/2 = 47 ∴ The average of fifth and sixth number is 47

The average of twelve numbers is 39. The average of the last five numbers is 35, and that of the first four numbers is 40. The fifth number is 6 less than the sixth number and 5 more than the seventh number. The average of the fifth and sixth numbers is:1. 442. 473. 504. 39

Answer» Correct Answer - Option 2 : 47

Given:

The average of twelve numbers = 39.

The average of the last five numbers = 35,

The average of the first four numbers = 40.

The fifth number is 6 less than the sixth number and 5 more than the seventh number.

Concept Used:

Sum = Average × total number

Solution:

The Sum of the twelve numbers = 12 × 39 = 468

The sum of the last five number = 5 × 35 = 175

The sum of the first four number = 4 × 40 = 160

The sum of the fifth, sixth and seventh number = (468 – 175 – 160) = 133

Let, the fifth number is x

Then, the sixth number is (x + 6) and the seventh number is (x – 5)

x + (x + 6) + (x – 5) = 133

⇒ 3x + 1 = 133

⇒ 3x = 132

⇒ x = 44

The fifth number is 44 and the sixth number is (44 + 6) = 50

Average of fifth and sixth number is (44 + 50)/2 = 47

∴ The average of fifth and sixth number is 47