Average - Study Mode

[#376] The average of ten numbers is 7. If each number is multiplied by 12, then the average of the new set of numbers is :
Correct Answer

(D) 84

Explanation

Solution: Average of 10 numbers = 7 Sum of these 10 numbers = (10 × 7) = 70 $$eqalign{
& herefore {x_1} + {x_2} + ..... + {x_{10}} = 70 cr
& Rightarrow 12{x_1} + 12{x_2} + ..... + 12{x_{10}} = 840 cr
& Rightarrow frac{{12{x_1} + 12{x_2} + ..... + 12{x_{10}}}}{{10}} = 84 cr} $$ ⇒ Average of new numbers is 84

[#377] The mean temperature of Monday to Wednesday was 37°C and of and of Tuesday to Thursday was 34°C. If the temperature on Thursday was $$frac{4}{5}$$ that of Monday, the temperature of Thursday was-
Correct Answer

(C) 36°C

Explanation

Solution: M + T + W = (37 × 3)°C = 111°C.....(i) T + W + Th = (34 × 3)°C = 102°C.....(ii) Subtracting (ii) from (i), we get: ⇒ M - Th = 9°C ⇒ M - $$frac{4}{5}$$M = 9 ⇒ $$frac{1}{5}$$ M = 9 ⇒ M = 45 ∴ Temperature on Thursday = $$ left( {frac{{4}}{{5}}} imes 45
ight) $$xa0°C = 36°C

[#378] The average weight of three boys A, B and C is $$54frac{1}{3}$$ kg, while the average weight of B, D and E is 53 kg. What is the average weight of A, B, C, D and E?
Correct Answer

(D) Data inadequate

Explanation

Solution: Total weight of (A + B + C) =( $$54frac{1}{3}$$ × 3 ) kg = 163 kg Total weight of (B + D + E) = (53 × 3) kg = 159 kg Adding both, we get: = A + 2B + C + D + E = (163 + 159) kg = 322 kg So, to find average weight of A, B, C, D and E, we ought to know B's weight, which is not given. So, the data is inadequate.

[#379] While calculating the average of a batsman as 36 in 100 matches that he played, one of the scores 90 was incorrectly noted as 40. The percentage error is-
Correct Answer

(D) 1.36%

Explanation

Solution: Correct sum = 36 × 100 + 90 - 40 = 3650 Correct average = $$frac{3650}{100}$$ = 36.5 Error = (36.5 - 36) = 0.5 ∴ Error % = ( $$frac{0.5}{36.5}$$ × 100 )% = $$frac{100}{73}$$% = 1.36%

[#380] The average of 8 numbers is 20. The average of first two numbers is $$15frac{1}{2}$$ and that of the next three is $$21frac{1}{3}$$. If the sixth number be less than the seventh and eighth numbers by 4 and 7 respectively, then the eight number is-
Correct Answer

(C) 25

Explanation

Solution: Let the eight number be x Then, sixth number = (x - 7) Seventh number = (x - 7) + 4 = (x - 3) So, $$ Leftrightarrow left( {2 imes 15frac{1}{2}}
ight) + left( {3 imes 21frac{1}{2}}
ight)$$ xa0 xa0 $$ + left( {x - 7}
ight)$$ xa0 $$ + left( {x - 3}
ight)$$ xa0 $$ + ,x = 8 imes 20$$ $$eqalign{
& Leftrightarrow 31 + 64 + left( {3x - 10}
ight) = 160 cr
& Leftrightarrow 3x = 75 cr
& Leftrightarrow x = 25 cr} $$