Question

The ratio of the number of chickens to the number of ducks on a farm was 3 : 8. There were 40 more ducks than chickens. When half the chickens and some of the ducks were sold, the ratio of the number of chickens to the number of ducks became 3 : 4. How many ducks were sold?

Answer 1

The number of ducks were sold be 48

Explanation:

Let the number of chicken be 3x and the number of ducks on a farm be 8x.

From the given conditions, it is states that there were 40 more ducks than chicken, i.e

8x+40=3x

or
`8x-3x=40`

or 5x=40

Simplify:

`x=8`

Then, the number of chicken be
`3x=3\cdot 8=24`

and the number of ducks be,
`8x=8\cdot 8=64`.

Since it is given that half the chicken and some of the ducks were sold ; then the ratio of the number of chicken to the number of ducks became 3:4

Let the number of ducks that were sold be y.

now by above condition, we have

`(12)/(64-y)= (3)/(4)`

then,

`12\cdot 4= 3\cdot (64-y)`

Simplify:

`48=192-3y` or

`3y=192-48` or

`3y=144`

On simplify we get,

y=48.

Therefore, the number of ducks were sold be, 48.