Average - Study Mode

[#331] The average age of A, B, C, D and E is 40 years. The average age of A and B is 35 years and the average of C and D is 42 years. Age of E is :
Correct Answer

(B) 46 years

Explanation

Solution: A + B + C + D + E = 40 × 5 = 200 A + B = 35 × 2 = 70 C + D = 42 × 2 = 84 Therefore, E = (A + B + C + D + E) - (A + B + C + D) E = 200 - 70 - 84 E = 46 years

[#332] The mean weight of 100 students in a class is 46 kg. The mean weight of boys is 50 and of girls is 40 kg. Therefore, the number of boys is:
Correct Answer

(B) 60

Explanation

Solution: Let number of boys are x and then number of girls = (100 - x) Thus, 50x + (100 - x) × 40 = 46 × 100 → x = 60 Number of boys = 60

[#333] There are three categories of jobs A, B and C. The average salary of the student who got the job of A and B categories is 26 lakh per annum. The average salary of the students who got the job of B and C category is 44 lakh per annum and the average salary of those students who got the job of A and C categories is 34 lakh per annum. The most appropriate (or closet) range of average salary of all the three categories (if it is known that each student gets only one category of jobs i.e. , A, B and C):
Correct Answer

(A) lies between 30 and 44

Explanation

Solution: Let the number of students who got the job of A, B and C categories is a, b and c respectively, Then the total salary, $$ = {frac{{left{ {26left( {a + b}
ight) + 44left( {b + c}
ight) + 34left( {c + a}
ight)}
ight}}}{{2left( {a + b + c}
ight)}}} $$ $$eqalign{
& = {frac{{left( {60a + 70b + 78c}
ight)}}{{2left( {a + b + c}
ight)}}} cr
& = frac{{left[ {30left( {a + b + c}
ight) + left( {5b + 9c}
ight)}
ight]}}{{left( {a + b + c}
ight)}} cr} $$ = 30 + some positive value Thus, the minimum salary must be Rs. 30 lakh and the maximum salary can not exceed 44, which is the highest of the three

[#334] The sum of the three consecutive even numbers is 44 more than the average of these numbers. Which of the following is the third largest of these numbers?
Correct Answer

(C) 24

Explanation

Solution: Let the numbers be x, x + 2 and x + 4 Then, ⇒ (x + x + 2 + x + 4) - $$frac{(x + x + 2 + x + 4)}{3}$$ xa0xa0 = 44 ⇒ (3x + 6) - $$frac{(3x + 6)}{3}$$ xa0 = 44 ⇒ 2 (3x + 6) = 132 ⇒ 6x = 120 ⇒ x = 20 ∴ Largest number = x + 4 = 24

[#335] The average of five consecutive odd numbers is 95. What is the fourth number in the descending order?
Correct Answer

91

Explanation

Solution: Let the numbers be x, x + 2, x + 4, x + 6 and x + 8 Then, $$ Rightarrow frac{{x + left( {x + 2}
ight) + left( {x + 4}
ight) + left( {x + 6}
ight) + left( {x + 8}
ight)}}{5} $$ xa0 xa0 xa0 xa0 $$= 95$$ $$eqalign{
& Rightarrow 5x + 20 = 475 cr
& Rightarrow 5x = 455 cr
& Rightarrow x = 91 cr} $$ So, the numbers are 91, 93, 95, 97 and 99 Clearly, the fourth number in the descending order is 93