Average - Study Mode

[#276] Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, then difference of first and third numbers is
Correct Answer

(D) 48

Explanation

Solution: Let the second number be x Then, first number = 2x, 3 rd number = 4x ∴ 2x + x + 4x = 56 × 3 ⇒ 7x = 168 ⇒ x = 24 ∴ Required difference = 4x - 2x = 2x = 2 × 24 = 48

[#277] The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3 : 5 : 7, the price of the cheapest item is-
Correct Answer

(A) Rs. 9000

Explanation

Solution: Let their prices be 3x, 5x and 7x respectively Then, ⇒ 3x + 5x + 7x = 15000 × 3 ⇒ 15x = 45000 ⇒ x = 3000 ∴ Cost of cheapest item = Rs. (3000 × 3) = Rs. 9000

[#278] 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.
Correct Answer

(C) 52.25

Explanation

Solution: Average marks $$eqalign{
& = left( {frac{{50 imes 40 + 60 imes 35 + 55 imes 45 + 45 imes 42}}{{40 + 35 + 45 + 42}}}
ight) cr
& = left( {frac{{2000 + 2100 + 2475 + 1890}}{{162}}}
ight) cr
& = left( {frac{{8465}}{{162}}}
ight) cr
& = 52.25 cr} $$

[#279] The mean of 5 observations is 60, the mean of 10 observations is 30 and the mean of 15 observations is 20. The mean of all the 30 observations is-
Correct Answer

(C) 30

Explanation

Solution: Required mean $$eqalign{
& = left( {frac{{60 imes 5 + 30 imes 10 + 20 imes 15}}{{5 + 10 + 15}}}
ight) cr
& = left( {frac{{300 + 300 + 300}}{{30}}}
ight) cr
& = left( {frac{{900}}{{30}}}
ight) cr
& = 30 cr} $$

[#280] In a class there are 32 boys and 28 girls. The average age of the boys in the class is 14 years and the average age of the girls in the class 13 years. What is the average age of the whole class (rounded to two digits after decimal) ?
Correct Answer

(D) 13.53

Explanation

Solution: Required average $$eqalign{
& = left( {frac{{32 imes 14 + 28 imes 13}}{{32 + 28}}}
ight) cr
& = left( {frac{{448 + 364}}{{60}}}
ight) cr
& = left( {frac{{812}}{{60}}}
ight) cr
& = 13.53 cr} $$