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

Question:A fraction becomes `2/3` when 1 is added to both, its numerator and denominator. And, it become `1/2` when 1 is subtracted from both the numerator and denominator. 

Let the required fraction be `x/y` then,

 `(x + 1)/(y + 1)`=`2/3`

 => 3x - 2y = -1  ...........(i)

 And, `(x -1)/(y - 1)`= `1/2`

 => 2x -y = 1  ...........(ii)

 Solving (i) & (ii), we get x = 3, y = 5.

 `:.`Required fraction =`3/5`

Question:The ratio of the ages of Mona and Sona is 4:5. Twelve years hence, their will be in the ratio of 5:6. What will be Sona's age after 6 years? 

Let their present ages ages be 4x & 6x

Then `(4x + 12)/(5x + 12)`=`5/6`

or x = 12

`:.` Sona's age after 6 years = (5x + 6) = 66 years

Question:Ramu was 4 times as old as his as his son 8 years age. After 8 years, Ramu will be twice as old his son. What are their present ages? 

Let son's age 8 years ago be x years.

 Then, Ramu's age at that time = 4x years.

 Son's age after 8 years = (x + 8) + 8 = (x + 16) years.

 Ramu's age after 8 years = (4x + 8) + 8 =(4x + 16) years.

 `:.` 2 (x + 16) = 4x + 16 

 or x = 8

 `:.` Son's present age = (x + 8) = (8 + 8) =16 years.

 `:.` Ramu's present age =(4x + 8) =(4 x 8 +8) =40 years.

Question:A man is four times as old as his son. Five years ago, the man was nine times as old as his son was at that time. What is the present age of the man? 

Let son's age = x.

 Then, man's age = 4x.

 9 (x -5) = (4x - 5)

 or 9x - 45 = 4x - 5

 or 5x = 40

 or x = 8

`:.` Man's present age = 4x = 4 x 8 = 32 years.