A number is 56 greater than the average of its third quarter and one twelfth. find it .

Explanation

Let the unknown number be 'x'
Let the sum of terms be 'S'
Let the no.of terms be 'n'
Let the average be 'A'
Average=(Sum of terms)/(Number of terms)
Sum of terms=One third of x+Quarter of x+One twelfth of x
`S=(x/3)+(x/4)+(x/12)`
`S=(4x+3x+x)/12`
`S=(8x)/12`
`S=(2x)/3`
`n=3`
`A=(2x)/3×(1/3)`
`A=(2x)/9`
The unknown number is 56 more than average
`x=56+((2x)/9)`
` x-((2x)/9)=56`
`(9x-2x)/9=56`
`((7x)/9)=56`
`7x=504`
`x=72`
The required number is `72`