Question

If 20 percent of 40 percent of a number is 10 greater than half the number, what is the number?

A. -500/21
B. -500/3
C. 200
D. 200/21
E. 210

Answer 1

0.2*0.4n = 0.5n + 10

0.08n = 0.5n + 10

-0.42n = 10

n = 10/-0.42

n = -500/21

Answer 2

Let the number be x.

40% of the number is =
`(x) ((40)/(100) )`

20% of 40% of the number is =
`(x)((40)/(100) )((20)/(100) )`

=
`(x)(0.4)(0.2)`

Given 20% of 40% of the number x is 10 greater than half the number x.

Half the number x =
`(x)/(2)`

So we can write the equation as ,

`(x)(0.4)(0.2) = (x)/(2) +10`

`(x)(0.08) = (0.5x)+10`

`(0.08x) = (0.5x) +10`

Now to find x, we will have to move (0.5x) to the left side by subtracting it from both sides. We will get,

`(0.08x) -(0.5x) = (0.5x) -(0.5x) +10`

`(0.08x) - (0.5x) = 10`

`(-0.42x) = 10`

Now to find x we will move (-0.42) to the right side by dividing it to both sides.

`((-0.42x))/((-0.42)) = (10)/((-0.42))`

`x = (10)/((-0.42))`

`x= -((10)(100))/(42)`

`x=- (1000)/(42)`

We will have to simplify 1000 and 42 by dividing the numerator and denominator by a common factor of it. 2 is a common factor of 1000 and 42.

So by dividing 1000 and 42 by 2 we will get,

`x = - (500)/(21)`

We have got the required answer here. Option A is the correct option here.