Question

If decreasing 120 by x% gives the same result as increasing 40 by x%, then x% of 210 is what percent less than (x+20)% of 180?........answer is (16 2/3%). but how

Answer 1

Answer:   x% of 210 is 20% percent less than (x+20)% of 180.

Step-by-step explanation:

Since we have given that

If decreasing 120 by x% gives the same result as increasing 40 by x%,

$120\times \dfrac{100-x}{100}=40\times \dfrac{100+x}{100}\\\\12(100-x)=4(100+x)\\\\3(100-x)=(100+x)\\\\300-3x=100+x\\\\300-100=x+3x\\\\200=4x\\\\x=\dfrac{200}{4}\\\\x=50$

So, x% of 210 is what percent less than (x+20)% of 180.

50% of 210 is what percent less than (50+20)% of 180

So, 50% of 210 is given by

$\dfrac{50}{100}\times 210\\\\=105$

and

$70\%\ of\ 180\\\\=\dfrac{70}{100}\times 180\\\\=0.7\times 180\\\\=126$

Now, our required percentage would be

$\dfrac{126-105}{105}\times 100\\\\=\dfrac{21}{105}\times 100\\\\=20\%$

Hence,  x% of 210 is 20% percent less than (x+20)% of 180.

Answer 2

Answer:

Step-by-step explanation: