model 6 find average of excluded number Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

Let the number of boys be x and that of girls be y.

∴ 71x + 73y = 71.8 (x + y)

⇒ 71.8x – 71x = 73y – 71.8y

⇒ 0.8x = 1.2y

⇒ $\text"x"/ \text"y"$ = ${1.2}/{0.8}$ = $12/8$ = $3/2$

∴ $\text"x"/\text"y"$+1 = $3/2$ + 1⇒ $\text"x+y"/ \text"y"$ = $5/2$

∴ Percentage of girls

= $\text"y"/ \text"x+y"$ × 100= $2/5$ × 100= 40%

Answer: (c)

Weight of teacher = 50 + 26 × 1 = 76 kg

Aliter : Using Rule 24,

( If a new member is added in a group then. age (or income) of added member = Average (or income) ± x (n + 1)

where x = increase (+) or decrease (–) in average age (or income) n = Number of members. )

Here, N = 50, T = 45, t = $1/10$ = 0.1

Weight of teacher = Average + × (n + 1)

= 50 + 1 (25 + 1)

= 50 + 26 = 76 kg

Answer: (b)

Sum of the three new numbers

= 8 × 8.5 – 5 × 7 = 68 – 35 = 33

∴ Required average = $33/3$ = 11