The average of 35 consecutive natural numbers is N. Dropping the first 10 numbers and including the next 10 numbers, the average is changed to M. If the value of M2 – N2 = 600, then the average of 3M and 5N is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 115
| Understanding | Application |
| We will use the concept of average.⇒ |
Let the first number of the 35 numbers be 'x' then it will form an A.P. ⇒x, x + 1, ..., x + 34 Average would be the middle term ⇒ x + 17 = N After the changes, the A.P. would change to ⇒ x + 10, x + 11, ..., x + 44 Average would be ⇒ x + 27 = M ⇒ M2 - N2 = 600 ⇒ (M + N)(M - N) = 600 ⇒ (x + 27 + x + 17)(x + 27 - x - 17) = 600 ⇒ (2x + 44) = 60 ⇒ x = 8 Average of 3M & 5N will be ⇒ (3M + 5N) / 2 ⇒ (3(x + 27) + 5(x + 17)) / 2 ⇒ (125 + 105) / 2 = 115 |