Three-fourths of a number is equal to 60\% of another number and the difference between these two numbers is 20 . What is the sum of these two numbers?
(a)170
(b)180
(c)220
(d)Cannot be determined
(e)None of these
Answer
Answer (as printed): B
Explanation
Let the numbers be $x$ and $x+20$. Then, $\frac{3}{4} x=60 \%$ of $(x+20)$ $\Rightarrow \frac{3}{4} x=\frac{60}{100}(x+20) \Rightarrow \frac{5}{4} x=x+20$ $\Rightarrow \frac{x}{4}=20 \Rightarrow x=20 \times 4=80$. ∴ Required sum $=x+x+20=2 x+20=2 \times 80+20$ $=180$.
Explanation as extracted from the printed page; notation may be imperfect.