Average - Study Mode

[#191] If the difference between the average of x, y and y, z is 12, then the difference between x and z is :
Correct Answer

(C) 24

Explanation

Solution: $$eqalign{
& Rightarrow frac{{x + y}}{2} - frac{{y + z}}{2} = 12 cr
& Rightarrow x + y - y - z = 24 cr
& Rightarrow x - z = 24 cr} $$

[#192] In an examination average marks obtained by the girls of a class is 85 and the average marks obtained by the boys of the same class is 87. If the girls and boys are in the ratio 4 : 5, average marks of the whole class (approx.) is closest to :
Correct Answer

(D) 86.1

Explanation

Solution: Average of whole class $$eqalign{
& = frac{{85 imes 4 + 87 imes 5}}{{5 + 4}} cr
& = frac{{340 + 435}}{9} cr
& = frac{{775}}{9} cr
& = 86.1 cr} $$

[#193] The average age of 40 students of a class is 15 years. When 10 new students are admitted, the average is increased by 0.2 year. The average age of the new students is :
Correct Answer

(B) 16 years

Explanation

Solution: Let the average age of the new students = x years According to the question, ⇒ 40 × 15 + 10x = 50 × 15.2 ⇒ 600 + 10x = 760 ⇒ 10x = 160 ⇒ x = 16 years

[#194] If a, b, c, d, e are five consecutive odd numbers, their average is :
Correct Answer

(D) $${ ext{a}} + 4$$

Explanation

Solution: Let five consecutive odd numbers are 1, 3, 5, 7, 9 Here, a = 1, b = 3, c = 5, d = 7, e = 9 According to the question, Average $$eqalign{
& = frac{{1 + 2 + 5 + 7 + 9}}{5} cr
& = frac{{25}}{5} cr
& = 5 cr} $$ Now check the option Option (D) a + 4 Here a = 1 1 + 4 = 5 satisfy

[#195] The average weight of 12 crewmen in a boat is increased by $$frac{1}{3}$$ kg, when one of the crewmen whose weight is 55 kg is replaced by a new man. What is the weight of that new man ?
Correct Answer

(D) 59 kg

Explanation

Solution: According to the question, Average weight of the 12 crewman increased by = $$frac{{1}}{3}$$ kg ∴ Total increase in weight $$eqalign{
& = 12 imes frac{1}{3} cr
& = 4{ ext{ kg}} cr} $$ Weight of old man = 55 kg Weight of new man = 55 + 4 = 59 kg