Question

I thought of a number, subtracted it from 6 1/4 , multiplied the difference by 1 2/3 and then by 2 4/5 . The result was the same as the result of division of 146 by 5 3/14 . What was my number?

Answer 1

Number was
`(1)/(4)`

Explanation:

Let the number was x.

As per statement of the question,

Subtracted from
`6(1)/(4)`

⇒
`6(1)/(4)` - x

⇒
`(25)/(4)-x`

Difference was multiplied by
`1(2)/(3)`

=
`((25)/(4)-x)* (1(2)/(3))`

=
`((25)/(4)-x)* ((5)/(3))`

Then again multiplied by
`2(4)/(5)` Or
`(14)/(5)`

=
`((25)/(4)-x)* ((5)/(3))* ((14)/(5))`

=
`((25)/(4)-x)* ((14)/(3))`

This result was same as the result of division of 146 by
`5(3)/(14)`

=
`(146)/((73)/(14))`

=
`(146* 14)/(73)`

= 28

Now
`((25)/(4)-x)* ((14)/(3))` = 28

`((25)/(4)-x)=((3* 28)/(14))`

`((25)/(4)-x)=6`

x =
`(25)/(4)-6`

=
`(25-24)/(4)`

=
`(1)/(4)`

=
`(1)/(4)`