Average - Study Mode

[#381] In an examination, a pupil’s average mark was 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?
Correct Answer

(D) 11

Explanation

Solution: Let the number of paper be x Then, pupil's total score = 63x ∴ $$frac{63x + 20 + 2}{x}$$ xa0 = 65 ⇒ 2x = 22 ⇒ x = 11

[#382] In a one-day cricket match the captain of one of the teams scored 30 runs more than the average runs scored by the remaining six batsman of that team who batted in the match. If the total runs scored by all the batsmen of that team were 310, how many runs did the captain score?
Correct Answer

(C) 70

Explanation

Solution: Let the average score of the remaining 6 batsmen be x runs. Then, sum of their scroe = 6x Captain's score = (x + 30) ∴ 6x + (x + 30) = 310 ⇒ 7x = 280 ⇒ x = 40 Hence, captain's score = x + 30 = 70

[#383] A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
Correct Answer

(A) Rs. 4991
(E) Rs. 4991

Explanation

Solution: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009 ∴ Required sale = Rs. [(6500 × 6) - 34009] = Rs. (39000 - 34009) = Rs. 4991

[#384] The average sale of car dealership was 15 cars per week. After a promotional scheme the average sale increased to 21 cars per week. The percentage increased in the sale of cars was-
Correct Answer

(B) 40%

Explanation

Solution: Number of cars sold per week originally = 15 × 7 = 105 Number of cars sold per week under scheme = 21 × 7 = 147 Increase in sale = 147 - 105 = 42 ∴ Percentage increase $$eqalign{
& = left( {frac{{42}}{{105}} imes 100}
ight)\% cr
& = left( {frac{{4200}}{{105}}}
ight)\% cr
& = 40\% cr} $$

[#385] The average age of the mother and her six children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother ?
Correct Answer

(B) 42 years

Explanation

Solution: Age of the mother = (12 × 7 - 7 × 6) years = 42 years