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

Question : 6 [SSC CPO 2010]

There are 50 students in a class. Their average weight is 45 kg. When one student leaves the class the average weight reduces by 100g. What is the weight of the student who left the class ?

a) 47.9 kg

b) 49.9 kg

c) 45 kg

d) 50.1 kg

Answer: (b)

Weight of the student who left = 50 × 45 – 49 × 44.9

= 2250 – 2200.1 = 49.9 kg.

Question : 7

The mean weight of 34 students of a school is 42 kg. If the weight of the teacher be included, the mean rises by 400 grams. Find the weight of the teacher (in kg).

a) 57 kg

b) 66 kg

c) 55 kg

d) 56 kg

Answer: (d)

Weight of the teacher = 42 kg. + ${35 × 400}/1000$kg

= 42 + 14 = 56 kg.

Aliter : Using Rule 24,

Here, x = $400/100$ = 0.4, n = 34

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

= 42 + 0.4 (34 + 1)

= 42 + 14 = 56 kg

Question : 8 [SSC FCI Assistant 2012]

The average of five numbers is 140. If one number is excluded, the average of the remaining four numbers is 130. The excluded number is :

a) 134

b) 180

c) 135

d) 150

Answer: (b)

Required number = 5 × 140 – 4 × 130

= 700 – 520 = 180

Aliter : Using Rule 25,

Here, x = (140 – 130) = 10, n = 5

Excluded number = Average + x (n – 1)

= 140 + 10 × 4 = 180

Question : 9 [SSC CGL Prelim 2005]

The average of marks of 28 students in Mathematics was 50; 8 students left the school, then this average increased by 5. What is the average of marks obtained by the students who left the school ?

a) 37.5

b) 42.5

c) 50.5

d) 45

Answer: (a)

Total marks of 28 students = 28× 50 = 1400

Total marks of 20 students = 20 × 55 = 1100

∴Total marks of 8 students = 1400 – 1100 = 300

∴ Average = $300/8$ = 37.5

Question : 10 [SSC CHSL 2011]

The average of six numbers is 32. If each of the first three numbers is increased by 2 and each of the remaining three numbers is decreased by 4, then the new average is

a) 34

b) 31

c) 35

d) 30

Answer: (b)

Change = 2×3 – 3 × 4 = – 6

∴ New average = 32 -$6/6$ = 31

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