model 6 find average of excluded number Practice Questions Answers Test with Solutions & More Shortcuts

Question : 11 [SSC CPO 2016]

The average of five numbers is 7. If three new numbers would be added, then the new average comes out to be 8.5. What is the average of those three new numbers?

a) 10.5

b) 11

c) 9

d) 11.5

Answer: (b)

Sum of three new numbers = 8 × 8.5 – 7 × 5

= 68 – 35 = 33

∴ Required average = $33/3$ = 11

Question : 12 [SSC CHSL 2012]

If the mean of 4 observations is 20, when a constant 'C’ is added to each observation, the mean becomes 22. The value of C is :

a) –2

b) 2

c) 6

d) 4

Answer: (b)

4C = 22 × 4 – 20 × 4 = 88 – 80 = 8

⇒ C = $8/4$ = 2

Question : 13

The average weight of 12 parcels is 1.8 kg. Addition of another new parcel reduces the average weight by 50 g. What is the weight of the new parcel ?

a) 1.10 kg

b) 1.15 kg

c) 1.50 kg

d) 1.01 kg

Answer: (b)

Total weight 12 parcels = 12 × 1.8 = 21.6 kg.

New average of 13 parcels = 1.8 – 0.05 = 1.75 kg.

Total weight of 13 parcels = 13 × 1.75 = 22.75 kg.

∴ Weight of new parcel = 22.75 – 21.6 = 1.15 kg.

Aliter : Using Rule 18,

( If in the group of N persons, a new person comes at the place of a person of 'T’ years, so that average age,

increases by 't’ years

Then, the age of the new person = T + N.t. )

Here, T = 1.8, N= (12 + 1) = 13, t = $50/1000$ = .05

Weight of new parcel = T – Nt

= 1.8 – 13 × 0.05

= 1.8 – 0.65 = 1.15 kg

Question : 14

The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is :

a) 27

b) 30

c) 25

d) 35

Answer: (d)

Total sum of five numbers = 27 × 5 = 135

Total sum of four numbers = 25 × 4 = 100

∴ Required number = 135 – 100 = 35

Question : 15 [SSC CGL Tier-I 2013]

The average of 50 numbers is 38. If two numbers namely 45 and 55 are discarded, the average of the remaining numbers is :

a) 32.5

b) 37.5

c) 35

d) 36

Answer: (b)

Required average = ${38 × 50 – 45 – 55}/48$

= $1800/48$ = 37.5

IMPORTANT quantitative aptitude EXERCISES

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