Average - Study Mode

[#66] A company produces on an average 4000 items per must for the first 3 months. How many items it must produce on an average per month over the next 9 months, to average 4375 items per month over the whole?
Correct Answer

(A) 4500

Explanation

Solution: Required average $$eqalign{
& = frac{{left( {4375 imes 12}
ight) - left( {4000 imes 3}
ight)}}{9} cr
& = frac{{52500 - 12000}}{9} cr
& = frac{{40500}}{9} cr
& = 4500 cr} $$

[#67] In a cricket eleven, the average age of eleven players is 28 years. Out of these, the average age of three groups of three players each are 25 years, 28 years and 30 years respectively. If in these groups the captain and the youngest player are not included and the captain is eleven years older than the youngest player, what is the age of the captain?
Correct Answer

(C) 35 years

Explanation

Solution: Sum of ages of the captain and the youngest player = [(28 × 11) - (25 × 3) + (28 × 3) + (30 × 3)] years = (308 - 249) years = 59 years Let the age of the youngest player be x years. Then, age of the captain = (x + 11) years ∴ x + (x + 11) = 59 ⇒ 2x = 48 ⇒ x = 24 So, the age of captain is = (x + 11) = (24 + 11) = 35 years

[#68] The mean monthly salary paid to 75 workers in a factory is Rs. 5680. The mean salary of 25 of them is Rs. 5400 and that of 30 others is Rs. 5700. The mean salary of the remaining workers is-
Correct Answer

(B) Rs. 6000

Explanation

Solution: Required average $$ = { ext{Rs}}{ ext{.}}$$ $$left[ {frac{{left( {5680 imes 75}
ight) - left{ {left( {5400 imes 25}
ight) + left( {5700 imes 30}
ight)}
ight}}}{{75 - left( {25 + 30}
ight)}}}
ight]$$ $$ = { ext{Rs}}{ ext{. }}left[ {frac{{426000 - left( {135000 + 171000}
ight)}}{{20}}}
ight]$$ $$eqalign{
& = { ext{Rs}}{ ext{. }}left( {frac{{120000}}{{20}}}
ight) cr
& = { ext{ Rs}}{ ext{. 6000}} cr} $$

[#69] There were 35 students in a hostel. If the number of the students is increased by 7, then the expenses of the mess increased by Rs. 42 per day, while the average expenditure per head diminishes by Rs. 1. The original expenditure of the mess per day was-
Correct Answer

(B) Rs. 420

Explanation

Solution: Let the original expenditure of the mess per day be Rs. x Then, new expenditure = Rs. (x + 42) $$eqalign{
& herefore frac{x}{{35}} - frac{{left( {x + 42}
ight)}}{{42}} = 1 cr
& Rightarrow 6x - 5left( {x + 42}
ight) = 210 cr
& Rightarrow x - 210 = 210 cr
& Rightarrow x = 420 cr} $$

[#70] The mean of 5 numbers is 18. If one number is excluded, their mean is 16. Find the excluded number.
Correct Answer

(B) 26

Explanation

Solution: Excluded number = (18 × 5) - (16 × 4) = 90 - 64 = 26