TNPSC Group 1, 2, 2a, 4, VAO Online Test - 1

Question: 1

In a class there are 50 students. Their average weight is 45 kg. When a student leaves the class, the average is reduced by 100 g. Find the weight of the student who left the class.

(A) 47.9 kg

(B) 49.9 kg

(C) 51.2 kg

(D) 54.3 kg

Ans: B

Total weight of 50 students = (45 × 50) kg = 2250 kg

Average weight of 49 students = (45 kg - 100 g) = 44.9 kg.

Total weight of 49 students = (44.9 × 49) kg = 2200.1 kg.

∴ Weight of the student who left the class = (2250 – 2200.1) = 49.9 kg.

Question: 2

A school has 4 sections of Chemistry in Class X having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.

(A) 50.25

(B) 51.25

(C) 52.05

(D) 52.25

Ans: D

Average marks = $$({50 × 40 + 60 × 35 + 55 × 45 + 45 × 42}/ {40 + 35 + 45 + 42})$$

                     = $$({2000 + 2100 + 2475 + 1890} / {162})$$

                     = $${8465}/{162}$$ = 52.25.

Question: 3

In a cricket eleven, the average age of eleven player is 28 years. Out of these, the average ages of three groups of three players each are 25 years, 28 years and 30 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player. What is the age of the captain?

(A) 33 years

(B) 34 years

(C) 35 years

(D) 36 years

Ans: C

Let the age of youngest player be x.

Then, age of the captain = ( x + 11)

∴ 3 x 25 + 3 x 28, + 3 x 30 + x + x + 11 = 11 x 28

⇒ 75 + 84 + 90 + 2x + 11 = 308

⇒ 2x = 48

⇒ x = 24.

∴ Age of the captain = (x + 11) = 35 years.

Question: 4

Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average of this eight member joint family is nearest to

(A) 20 years

(B) 22 years

(C) 24 years

(D) 25 years

Ans: C

Sum of the ages of all 8 members 10 years ago = 231 years.

Sum of the ages of all members, 7 years ago

= (231 + 8 × 3 – 60) years = 195 years.

Sum of the ages of all members, 4 years ago

= (195 + 8 × 3 – 60) years = 159 years.

Sum of the present ages of all 8 members

= (159 + 8 × 4) years = 191 years.

Current average age = $$({191}/{8})$$ years.

= 23.8 yeas ≈ 24 years(appr).

Question: 5

If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55 and 60 then the average marks of all the students is

(A) 39.68

(B) 53.33

(C) 54.68

(D) 55

Ans: A

Average marks of all students = $${55 × 50 + 60 × 15 + 45 × 60} / {160}$$

                                          = $${55 × 5 + 6 × 15 + 45 × 6} / {16}$$

                                          = $${275 + 90 + 270} / {16}$$ = $${635} / {16}$$ = 39.68.

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