Average - Study Mode

[#356] The average age of 30 students in a class is 15 years. If 6 students of this class have the average age of 16 years, then the average age of the remaining 24 students would be-
Correct Answer

(D) 14 yrs 9 mths

Explanation

Solution: Sum of the ages of 24 students = (15 × 30) - (16 × 6) = 450 - 96 = 354 ∴ Required average = $$left( {frac{{354}}{{24}}}
ight)$$ = $$14frac{3}{4}$$ yrs = 14 yrs 9 mths

[#357] Of the four numbers, the first is twice the second, the second is one-third of the third and the third is 5 times the fourth. The average of the numbers is 24.75. The largest of these numbers is-
Correct Answer

(D) None of these

Explanation

Solution: Let the fourth number be x Then, third number = 5x Second number = $$frac{5x}{3}$$ and First number = $$frac{10x}{3}$$ x + 5x + $$frac{5x}{3}$$ xa0+ $$frac{10x}{3}$$ xa0 = (24.75 × 4) ⇒ 11x = 99 ⇒ x = 9 So, the numbers are 9, 45, 15 and 30 ∴ Largest number = 45

[#358] A car owner buys petrol at Rs. 17, Rs. 19 and Rs. 20 per litre for three consecutive years. Compute the average cost per litre, if he spends Rs 6460 per year.
Correct Answer

(B) Rs. 18.58

Explanation

Solution: Total quantity of petrol consumed in 3 years = $$left( {frac{{6460}}{{17}} + frac{{6460}}{{19}} + frac{{6460}}{{20}}}
ight)$$ xa0 litres = (380 + 340 + 323) litres = 1043 litres Total amount spent = Rs. (3 × 6460) = Rs. 19380 ∴ Average cost = Rs. $$left( {frac{{19380}}{{1043}}}
ight)$$ = Rs. 18.58

[#359] The average of five consecutive numbers is x. If the next two numbers are included, how shall the average vary?
Correct Answer

(A) It shall increase by 1

Explanation

Solution: Let the five consecutive numbers be z, z + 1, z + 3 and z + 4 Then, $$ Rightarrow frac{{z + left( {z + 1}
ight) + left( {z + 2}
ight) + left( {z + 3}
ight) + left( {z + 4}
ight)}}{5} = x$$ $$eqalign{
& Rightarrow 5z + 10 = 5x cr
& Rightarrow z = frac{{5x - 10}}{5} cr
& Rightarrow z = x - 2 cr} $$ So, the numbers are x - 2, x - 1, x, x + 1, x + 2 ∴ Required mean $$ = frac{{left( {x - 2}
ight) + left( {x - 1}
ight) + x + left( {x + 1}
ight) + left( {x + 2}
ight) + left( {x + 3}
ight) + left( {x + 4}
ight)}}{7}$$ $$eqalign{
& = frac{{7x + 7}}{7} cr
& = x + 1 cr} $$

[#360] In a certain factory there are five workers A, B, C, D and E. A can complete a work in 4 minutes, B in 5 minutes, C in 6 minutes, D in 10 minutes and E in 12 minutes. The average number of units of work completed per worker per minute will be-
Correct Answer

(A) 0.16

Explanation

Solution: Number of units of work completed by the five workers in 1 minute: $$eqalign{
& A o frac{1}{4}, cr
& B o frac{1}{5}, cr
& C o frac{1}{6}, cr
& D o frac{1}{{10}}, cr
& E o frac{1}{{12}} cr} $$ ∴ Required average $$eqalign{
& = frac{{left( {frac{1}{4} + frac{1}{5} + frac{1}{6} + frac{1}{{10}} + frac{1}{{12}}}
ight)}}{5} cr
& = left( {frac{4}{5} imes frac{1}{5}}
ight) cr
& = frac{4}{{25}} cr
& = 0.16 cr} $$