Average - Study Mode

[#196] The average of 20 numbers is 12. The average of the first 12 numbers is 11 and that of the next 7 numbers is 10. The last number is ?
Correct Answer

(B) 38

Explanation

Solution: Let the last number = x According to the question, ⇒ 12 × 11 + 7 × 10 + x = 20 × 12 ⇒ 132 + 70 + x = 240 ⇒ x = 240 - 202 ⇒ x = 38

[#197] The average of seven numbers is 18. If one of the numbers is 17 and if it is replaced by 31, then the average becomes :
Correct Answer

(C) 20

Explanation

Solution: According to the question, Actual number = 17 New number = 31 Difference = 31 - 17 = 14 Difference '14' effects the seven numbers = $$frac{14}{7}$$ = 2 ∵ Present average = 18 ∴ New average = 18 + 2 = 20

[#198] The average daily income of 7 men, 11 women and 2 boys is Rs. 257.50. If the average daily income of the men is Rs. 10 more than that of women and the average daily income of the women is Rs. 10 more than that of boys the average daily income of a man is -
Correct Answer

(C) Rs. 265

Explanation

Solution: Let per day income of boy, women, man are = x, x + 10, x + 20 According to the question, $$ Rightarrow frac{{7M + 11W + 2B}}{{20}}$$ xa0 xa0= 257.50 $$ Rightarrow 7left( {x + 20}
ight) + 11left( {x + 10}
ight) + 2x$$ xa0 xa0 xa0 = 257.50 × 20 $$ Rightarrow 7x + 140 + 11x + 110 + 2x$$ xa0 xa0 xa0 = 5150 $$eqalign{
& Rightarrow 20x = 5150 - 250 cr
& Rightarrow x = frac{{4900}}{{20}} cr
& Rightarrow x = 245 cr} $$ Per day income of man = x + 20 = 245 + 20 = 265

[#199] The average age of 11 players of a cricket team is increased by 2 months when two of them aged 18 years and 20 years are replaced by two new players. The average age of the new players is :
Correct Answer

(C) 19 years 11 months

Explanation

Solution: Total age of 2 players = 18 + 20 = 38 years Increased years = 2 × 11 = 22 months Age of new players = 38 years + 22 months = 39 years 10 months Average = 19 years 11 months Alternate Let the total age of 11 players = 11x Then the sum of age of new players = y years According to the question, $$eqalign{
& Rightarrow 11x + y - 18 - 20 = 11left( {x + frac{1}{6}}
ight) cr
& Rightarrow 11x + y - 38 = 11x + frac{{11}}{6} cr
& Rightarrow y = frac{{11}}{6} + 38 cr
& Rightarrow y = frac{{239}}{6} cr} $$ ∴ Average $$eqalign{
& = frac{{239}}{{2 imes 6}} cr
& = frac{{239}}{{12}} cr} $$ = 19 years 11 months

[#200] The average of six numbers is 32. If each of first three numbers is increased by 2 and each of the remaining three numbers is decreased by 4, then the new average is ?
Correct Answer

(C) 31

Explanation

Solution: According to the question, First three numbers is increased by 2 = 3 × 2 = + 6 Remaining three numbers is decreased by 4 = (- 4 × 3) = - 12 Difference '- 6' effect on 6 numbers = $$frac{- 6}{+ 6}$$ xa0 = - 1 ∴ Previous average = 32 New average = 32 - 1 = 31