model 1 basic average questions Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

Answer: (c)

Answer: (c)

The average of m numbers = n²

Total number of ‘m’ numbers = m × n²

And the average of n numbers = m²

Total number of ‘n’ numbers = n × m²

∴ Average of (m + n) numbers

= ${mn² + m²n}/{m + n} = {mn(n + m)}/{m + n} = mn$

Answer: (a)

According to the question let m = 1

∴ 5 consecutive integers are = 1,2,3,4,5

$\text"1+2+3+4+5"/5=n$

$n = 15/5=3$

6 consecutive integers starting with (m + 2) are = 3,4,5,6,7,8

∴$\text"3+4+5+6+7+8"/6=33/6=11/2$

Now check from option to put n = 3

While in Option :(a) $\text"2n+5"/2 = 11/2 $

Answer: (d)

Given,

$\text"(a + a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + 6 + a + 7 + a + 8)"/9 = n$

$=> \text"(9a + 36)"/9 = n$

=> a + 4 = n -------------------- ( 1 )

If the next 2 numbers are included , let new average = k

$\text"(a + a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + 6 + a + 7 + a + 8 + a + 9 + a + 10)"/11 = k$

$\text"(11a + 55)"/11 = k$

a + 5 = k -------------------- ( 2 )

Subtracting ( 1 ) from ( 2 ) , we get :

a + 5 - a - 4 = k - n

=> k - n = 1

=> k = n + 1

Therefore the new average is n + 1

Answer: (b)

According to the question consecutive even numbers = a, b, c, d, e, f, g

Consecutive odd numbers = j, k, l, m, n

Consecutive even number = 2, 4, 6, 8, 10, 12, 14

$\text"2+4+6+8+10+12+14"/7=56/7=8$ middle term

Consecutive odd numbers 1, 3, 5, 7, 9

$\text"1+3+5+7+9"/5=25/5$ middle term

Same as in the above situation.

Average of a, b, c, d, e, f, g = d

Average of j, k, l, m, n, = l

∴ Required average = ${d+l}/2$