Average - Study Mode

[#106] There are three positive numbers. One third of the average of all the three numbers is 8 less than the value of the highest number. The average of the lowest and the second lowest number is 8. What is the highest number?
Correct Answer

(A) 11

Explanation

Solution: Let the three positive numbers in increasing order be a, b and c and the average of these numbers be be A. Then, $$frac{{a + b + c}}{3} = A.....(i)$$ Given, $$eqalign{
& c - frac{A}{3} = 8 cr
& Rightarrow c - frac{{a + b + c}}{9} = 8.....(ii) cr} $$ Also given, $$eqalign{
& frac{{b + a}}{2} = 8 cr
& Rightarrow a + b = 16.....(iii) cr} $$ Putting the value of (a + b) in equation (ii), we get $$eqalign{
& Rightarrow c - left( {frac{{16 + c}}{9}}
ight) = 8 cr
& Rightarrow 9c - 16 - c = 72 cr
& Rightarrow 8c = 72 + 16 cr
& Rightarrow 8c = 88 cr
& Rightarrow c = 11 cr} $$ ∴ Highest number = 11

[#107] Average score of a class of 60 students, in an exam, was 43. Average score of the students who had passed is 52 and the average score of students who had failed is 16. How many failed the exam?
Correct Answer

(C) 15

Explanation

Solution: Total number of students in class = 60 Average score of passed student = 52 Average score of failed students = 16 By applying the rule of alligation, ∴ Number of students who failed in exam = $$frac{1}{4}$$ × 60 = 15

[#108] The average weight of boys in a class is 30 kg and the average weight of girls in the same class is 20 kg. If the average weight of the whole class is 23.25 kg, what could be the possible strength of boys and girls respectively in the same class?
Correct Answer

(B) 13 and 27

Explanation

Solution: Let the number of boys and girls in the class are x and y. According to given information, ⇒ 30x + 20y = 23.25 (x + y) ⇒ 30x + 20 y = 23.25x + 23.25y ⇒ 30x - 23.25x = 23.25y - 20y ⇒ 6.75x = 3.25y ⇒ $$frac{x}{y}$$ = $$frac{3.25}{6.75}$$ ⇒ $$frac{x}{y}$$ = $$frac{13}{27}$$ Hence, possible number of boys and girls 13 and 27 respectively.

[#109] The mean monthly salary paid to graduating MBA class of a management institute is Rs. 16000. The mean monthly salary paid to students with work experience is Rs. 18000. The corresponding figure for the students without any work experience is Rs. 12000. Determine the percentage of students with work experience and those without any work experience in the class.
Correct Answer

(A) 66.67%, 33.33%

Explanation

Solution: Let the number of students with work experience be x and those without work experience be y. Then, 18000x + 12000y = 16000 (x + y) ⇒ 2000x = 4000y ⇒ $$frac{x}{y}$$ = $$frac{2}{1}$$ ∴ Percentage of students with work experience = $$left( {frac{2}{3} imes 100}
ight)\% $$ = 66.67% Percentage of students without work experience = (100 - 66.67)% = 33.33%

[#110] The monthly incomes of five persons are Rs. 1132, Rs. 1140, Rs. 1144, Rs. 1136 and Rs. 1148 respectively. What is their arithmetic mean?
Correct Answer

(D) Rs. 1140

Explanation

Solution: Arithmetic mean $$eqalign{
& = { ext{Rs}}{ ext{. }}left( {frac{{1132 + 1140 + 1144 + 1136 + 1148}}{5}}
ight) cr
& = { ext{Rs}}{ ext{.}}left( {frac{{5700}}{5}}
ight) cr
& = { ext{Rs}}{ ext{. 1140}} cr} $$