General Mathematics

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? 
AnswerLet 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

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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? 
AnswerLet 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

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

Then `30/100`x = 12.6

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

`:.` Required number = 42

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

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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. 
AnswerLet 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

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