model 1 basic average questions Practice Questions Answers Test with Solutions & More Shortcuts

Question : 26 [SSC Constable 2015]

The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. The weight of the new person is

a) 76 kg

b) 76.5 kg

c) 85 kg

d) 84 kg

Answer: (c)

Weight of new person

= (65 + 8 × 2.5) kg

= (65 + 20) kg

= 85 kg

Aliter : Using Rule 23,

Here, x = 2.5, n = 8

Weight of new person

= weight of replaced boy + x × n

Question : 27 [SSC Data Entry Operator2009]

The average marks of 32 boys of section A of class X is 60 whereas the average marks of 40 boys of section B of class X is 33. The average marks for both the sections combined together is

a) 46$1/2$

b) 45$1/2$

c) 45

d) 44

Answer: (c)

Required average

${32×60+33×40}/72$

${1920+1320}/72$ = $3240/72$ = 45

Question : 28 [SSC CGLTier-I 2013]

The average of 20 numbers is 15 and the average of first five is 12. The average of the rest is

a) 14

b) 13

c) 15

d) 16

Answer: (d)

If the average of remaining numbers be x, then

20 × 15 = 5 × 12 + 15x

⇒ 300 = 60 + 15x

⇒ 15x = 300 – 60 = 240

⇒ x = $240/15$ = 16

Aliter : Using Rule 13,

Here, m = 20, x = 15

n = 5, y = 12

Average of remaining Numbers = $({mx-ny}/{m-n})$

= $({20×15-5×12}/{20-5})$

= $({300-60}/15)$ = $240/15$ = 16

Question : 29

The average of marks obtained by 100 candidates in a certain examination is 30. If the average marks of passed candidates is 35 and that of the failed candidates is 10, what is the number of candidates who passed the examination?

a) 80

b) 90

c) 70

d) 60

Answer: (a)

Number of successful students in the exam = x

∴ Number of unsuccessful students = 100 – x

According to the question,

30 = ${35x+10(100-x)}/100$

⇒ 3000 = 35x + 1000 – 10x

⇒ 3000 = 25x + 1000

⇒ 25x = 3000 – 1000 = 2000

⇒ x = $2000/25$ = 80

Question : 30 [SSC Section Officer 2007]

The average of 30 numbers is 15. The average of the first 18 numbers is 10 and that of the next 11 numbers is 20. The last number is

a) 60

b) 50

c) 52

d) 56

Answer: (b)

Let the last number be x.

According to the question,

18 × 10 + 11 × 20 + x = 30 × 15

⇒ 180 + 220 + x = 450

⇒ 400 +x = 450

⇒ x = 450 – 400 = 50

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