Average - Study Mode

[#121] The average of 80 boys in a class is 15. The average age of a group of 15 boys in the class is 16 and the average age of another 25 boys in the class is 14. What is the average age of the remaining boys in the class?
Correct Answer

(C) 15.25

Explanation

Solution: Required average $$eqalign{
& = frac{{left( {15 imes 80}
ight) - left[ {left( {16 imes 15}
ight) + left( {14 imes 25}
ight)}
ight]}}{{80 - left( {15 + 25}
ight)}} cr
& = frac{{1200 - left( {240 + 350}
ight)}}{{40}} cr
& = frac{{610}}{{40}} cr
& = 15.25 cr} $$

[#122] The average of 6 observations is 45.5. If one new observation is added to the previous observations, then the new average becomes 47. The new observation is-
Correct Answer

(C) 56

Explanation

Solution: New observation = (47 × 7) - (45.5 × 6) = 329 - 273 = 56

[#123] If the average temperature of first four days of the week was 39°C and the average temperature of the week was 40°C, then what was the average temperature of the last three days of the week?
Correct Answer

(C) 41.3°C

Explanation

Solution: Required average $$eqalign{
& = {left[ {frac{{left( {40 imes 7}
ight) - left( {39 imes 4}
ight)}}{3}}
ight]^ circ }{ ext{C}} cr
& = {left( {frac{{124}}{3}}
ight)^ circ }{ ext{C}} cr
& = {41.3^ circ }{ ext{C}} cr} $$

[#124] The average weight of 3 men A, B, and C is 84 kg. Another man D joins the group and the average now becomes 80 kg. If another man E, whose weight is 3 kg more than that of D, replaces A, then the average weight of B, C, D and E becomes 79 kg. The weight if A is-
Correct Answer

(C) 75 kg

Explanation

Solution: Let A, B, C, D and E represent their respective weights. Then, A + B + C = (84 × 3) = 252 kg A + B + C + D = (80 × 4) = 320 kg ∴ D = (320 - 252) kg = 68 kg E = (68 + 3) kg = 71 kg B + C + D + E = (79 × 4) = 316 kg Now, = (A + B + C + D) - (B + C + D + E) = (320 - 316) kg = 4 kg ∴ A - E = 4 ⇒ A = (4 + E) ⇒ A = 75 kg

[#125] A team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If had scored 92 points, the average score for the team would have been 84. The number of points, the team scored was-
Correct Answer

(C) 665

Explanation

Solution: Let the total score be x $$eqalign{
& herefore frac{{x + 92 - 85}}{8} = 84 cr
& Rightarrow x + 7 = 672 cr
& Rightarrow x = 665 cr} $$