Average - Study Mode
[#166] Out of nine persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was :
Correct Answer
(C) Rs. 292.50
Explanation
Solution: Let the average of 9 people expenditure = Rs. x According to the question, ⇒ $$frac{30 × 8 + x + 20}{9}$$ xa0xa0 = x ⇒ 240 + 20 + x = 9x ⇒ 260 = 8x ⇒ x = $$frac{260}{8}$$ ⇒ x = 32.5 Total expenditure are = 32.5 × 9 = Rs. 292.50
[#167] A man had 7 children. When their average age was 12 years, a child aged 6 years died. Then average age of remaining six children is :
Correct Answer
(A) 13 years
Explanation
Solution: According to the question, Average age of 7 children = 12 years Sum of ages of 7 children = 84 years If a child aged 6 years died then Sum of aged of 6 children = 84 - 6 = 78 years ∴ Average = $$frac{78}{6}$$ = 13 years
[#168] In a class, the average score of girls in an examination is 73 and that of boys is 71. The average score for the whole class is 71.8. Find the percentage of girls :
Correct Answer
(A) 40%
Explanation
Solution: Let the number of girls = x And, the number of boys = y According to the question, 73x + 71y = 71.8 (x + y) 1.2x = 0.8y $$frac{x}{y}$$ = $$frac{2}{3}$$ ∴ Girls% = $$frac{2}{2 + 3}$$ × 100 = $$frac{2}{5}$$ × 100 = 40%
[#169] If the average of 6 consecutive even number is 25, the difference between the largest and the smallest number is :
Correct Answer
(B) 10
Explanation
Solution: According to the question, Sum of 6 consecutive even number is = 25 × 6 = 150 Sn = $$frac{n}{2}$$ [2a +(n - 1) × d] ⇒ 150 = $$frac{6}{2}$$ [2a + (6 - 1) × 2] ⇒ 150 = $$frac{6}{2}$$ (2a + 10) ⇒ 300 = 12a + 60 ⇒ 12 a = 240 ⇒ a = $$frac{240}{12}$$ ⇒ a = 20 ∴ Numbers are 20, 22, 24, 26, 28, 30 Difference between largest and smallest is = 30 - 20 = 10 Alternate : Let the 6 consecutive number is = x, x + 2, x + 4, x + 6, x + 8, x + 10 According to the question, Largest number = Average + (n - 1) = 25 + 5 = 30 Smallest number = Average - (n - 1) = 25 - 5 = 20 Difference between largest and smallest number = 30 - 20 = 10
[#170] The sum of three consecutive even numbers is 28 more than the average of these three number. Then the smallest of these number is -
Correct Answer
(C) 12
Explanation
Solution: Let consecutive even number x, x + 2, x + 4 According to the question, (x + x + 2 + x + 4) - $$frac{(x + x + 2 + x +4)}{3}$$ $$frac{3(3x + 6) - (3x + 6)}{3}$$ xa0xa0 = 28 2 (3x + 6) = 28 × 3 3x + 6 = 42 3x = 36 x = 12 So, smallest number = x = 12