# Over one year a company's sales increased 20% and its expenses decreased 20%. The ratio of sales to expenses at the end of that year was how many times the ratio at the beginning of that year?

Aug 29, 2016

The ratio is $1.5$ times the ratio at the beginning of that year.
Let ${s}_{1} , {s}_{2}$ be the sales at beginning and 1 year after.
and ${e}_{1} , {e}_{2}$ be the expenses at beginning and 1 year after.
Due to increased sale by 20%:. s_2 =1.2*s_1 and
Due to decreased expenses by 20%:. e_2 =0.8*e_1 :. s_2/e_2=(1.2*s_1)/(0.8*e_1)= 1.5*(s_1/e_1):.The ratio of sale and expenses is $1.5$ times the ratio at the beginning of that year.[Ans]