Question

A designer increased the area of a tapestry by 20%. By what percent the width of tapestry was decreased in the process, if its length was increased by 50%?

Answer 1

The answer is decreased by 20%.

Explanation:

Answer 2

By 20% the width of tapestry was decreased in the process.

Explanation:

Given : A designer increased the area of a tapestry by 20% and length was increased by 50%?

To find : By what percent the width of tapestry was decreased in the process?

Solution : Let the length and width of the tapestry is l and w respectively.

So, The area of tapestry is
`A=l* w`

According to question,

A designer increased the area of a tapestry by 20%.

i.e, The new area is
`A_N= lw+20\% ( lw)`

`A_N= lw+(1)/(5) (lw)=(6)/(5)lw`

And length was increased by 50%

i.e, The new length is
`l= l+50\% l`

`l= l+(1)/(2)l=(3)/(2)l`

and let the new width is w'

Then the area is
`A=(3)/(2)lw'`

So, to find the new width is

Area = New area

`(3)/(2)lw'=(6)/(5)lw`

`w'=(12)/(15)w`

The percentage of width of tapestry decreased is

`\% change= (1-w')* 100`

`\% change= (1-(12)/(15)w)* 100`

`\% change=(3)/(15)w* 100`

`\% change=20\%w`

Therefore, By 20% the width of tapestry was decreased in the process.