Average - Study Mode

[#116] The average age of all the students of a class is 18 years. The average age of boys of the class is 20 years and that of the girls is 15 years. If the number of girls in the class is 20, then find the number of boys in the class.
Correct Answer

(B) 30

Explanation

Solution: Let the number of boys in the class be x Then, ⇒ 18(x + 20) = 20x + 15 × 20 ⇒ 18x + 360 = 20x + 300 ⇒ 2x = 60 ⇒ x = 30

[#117] In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to each the target of 282 runs?
Correct Answer

(A) 6.25

Explanation

Solution: Required run rate $$eqalign{
& = frac{{282 - left( {3.2 imes 10}
ight)}}{{40}} cr
& = frac{{250}}{{40}} cr
& = 6.25 cr} $$

[#118] If the average of 5 numbers is 10, the number which should be added to make the average 12 is-
Correct Answer

(C) 22

Explanation

Solution: Required number = (12 × 6) - (10 × 5) = 72 - 50 = 22

[#119] The batting average for 40 innings of a cricket player is 50 runs. His highest score exceeds his lowest score by 172 runs. If these two innings are excluded, the average of the remaining 38 innings is 48 runs. The highest score of the player is
Correct Answer

(D) 174 runs

Explanation

Solution: Let the highest score be x Then, lowest score = (x - 172) Then, ⇔ (50 × 40) - [x + (x - 172)] = 38 × 48 ⇔ 2x = 2000 + 172 - 1824 ⇔ 2x = 348 ⇔ x = 174

[#120] The average marks of a student in 8 subjects is 87. Of these, the highest marks are 2 more than the one next in value. If these two subjects are eliminated, the average marks of the remaining subjects are 85. What are the highest marks now obtained by him?
Correct Answer

(C) 94

Explanation

Solution: Let the highest marks obtained by the student be x Then, second highest marks = x - 2 Sum of marks of these 2 subjects = (87 × 8) - (85 × 6) = 696 - 510 = 186 ∴ x + (x - 2) = 186 ⇒ 2x = 188 ⇒ x = 94