Question:The average of 11 results is 60. If the average of first six results is 58 and the last six is 63, find the sixth result. 

Sixth result 

`= (6 xx 58 + 6 xx 63 - 11 xx 60)` 

`= 66`

Question:Distance between two stations A and B is 778 km. Hari Mohan covers the journey from A to B at 84 km per hour and return back to A with a uniform speed of 56 km per hour. Find his average speed during the whole journey. 

Required average speed = `(2xy)/(x + y)` km/hr.

= `(2 xx 84 xx 56)/(84 xx 56)` km/hr.

=`((2 xx 84 xx 56)/140)` km/hr

=67.2 km/hr

Question:There are two sections A and B of a class, considering of 36 and 44 students respectively. If the average weight of section A is 40 kg and that of section B is 35 kg, find the average weight of the whole class. 

Total weight of (36 + 44) students

 =(36 x 40 +44 x 35) kg =2980 kg.

 `:.` Average weight of the whole class =`2980/80` kg

 =37.25 kg.

Question:The average weight of A, B, C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, find the weight of the whole class. 

A + B + C = (45 x 3) kg =135 kg.
A + B = (40 x 2) =80 kg & B + C =(43 x 2) = 86 kg.
`:.` B = (A + B) + (B + C) - (A + B + C) = (86 + 80 - 135) kg = 31 kg.

Question:A batsman makes a scores of 87 runs in the 17th inning and thus increase his average by 3. Find his average after 17th inning. 

Let the average after 17th inning = x.
Then, average after 16th inning= (x-3).
`:.` 16 (x -3) + 87 =17x.
or x = (87 - 48)
= 39 
=

Question:Nine persons went to a hotel for taking their meals. Eight of them spent Rs. 12 each on their meals and the ninth spent Rs 8 more than the average expenditure of all the nine. What was the total money spent by them? 

Let the expenditure be x.

Then, average =`x/9`

`:.` `8 xx 12 +(x/9 + 8)` = x

or `x - (x/9)` = 104.

or `(8x)/9` = 104

or x =`((104 xx 9)/8)` = 117

Question:There were 35 students in a hostel. Due to the admission of 7 new students, the expenses of the mess were increased by Rs 42 per day while the average expenditure per head diminished by Re 1. What was the original expenditure of the mess? 

Let the total average expenditure be Rs. x then,
42 (x - 1) - 35x = 42
=> 7x = 84
=> x = 12
`:.` Origanl expenditure = Rs (35 x 12) = Rs 420

Question:If 30% of a certain number is 12.6, then find the number. 

Let the required number be x.

Then `30/100`x = 12.6

or x= `((12.6 xx 100)/30)` =42

`:.` Required number = 42

Question:The average of four consecutive even numbers is 27. Find the largest of these numbers. 

Let the four consecutive even numbers be x, x + 2, x + 4, x + 6.
Their total sum =(27 x 4) = 108

`:.` x + x + 2 + x + 4 + x + 4 + x + 6 = 108

or 4x = 96

or x = `96/4`

or x = 24

 `:.` Largest number = (x + 6) = (24 + 6) = 30

Question:A number consists of two digits. The sum of the digit is 9. If 63 is subtracted from the number, its digits are interchanged. Find the number. 

Let ten's digit = x

Then, total sum = (27 x 4) = 108

`:.` x + x + 2 + x + 4 + x + 6 =  108

or 4x = 96

or x =`96/4`

x = 24
 
`:.` Largest number =(x + 6) = (24 + 6) =30