Question

when y is decreased by ten percent the result is equal to fifteen percent of x .Assuming both x and y are non zero what is the ratio of x to y?​

Answer 1

Given:-

when y is decreased by 10% the result is equal to 15% of x.

To find:-

the ratio of x to y

Solution:-

ATQ,

y - 10% of y = 15% of x

= $\sf{y - \dfrac{10}{100}\times y = \dfrac{15}{100}\times x}$

= $\sf{y - \dfrac{10y}{100} = \dfrac{15x}{100}}$

= $\sf{y - \dfrac{y}{10} = \dfrac{15x}{100}}$

= $\sf{\dfrac{10y - y}{10} =\dfrac{15x}{100}}$

= $\sf{\dfrac{9y}{10} = \dfrac{15x}{100}}$

= $\sf{9y = \dfrac{15x\times10}{100}}$

= $\sf{9y = \dfrac{15x}{10}}$

= $\sf{9y\times 10 = 15x}$

= $\sf{90y = 15x}$

= $\sf{\dfrac{90}{15} = \dfrac{x}{y}}$

= $\sf{\dfrac{x}{y} = \dfrac{6}{1}}$

$\sf{\implies x:y = 6:1}$

Therefore ratio of x to y is 6:1.