Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: 2005 · Marks: · Difficulty:
Two numbers are in the ratio $1 \frac{1}{2}: 2 \frac{2}{3}$. When each of these is increased by 15, their ratio becomes $1 \frac{2}{3}: 2 \frac{1}{2}$. The greater of the numbers is
(a)27
(b)36
(c)48
(d)64
Answer
Answer (as printed): C
Explanation
Ratio of numbers $=1 \frac{1}{2}: 2 \frac{2}{3}=\frac{3}{2}: \frac{8}{3}=9: 16$. Let the numbers be $9 x$ and $16 x$. $$\text { Then, } \frac{9 x+15}{16 x+15}=\frac{\left(1 \frac{2}{3}\right)}{\left(2 \frac{1}{2}\right)}=\frac{5}{3} \times \frac{2}{5}=\frac{2}{3}$$ $\Rightarrow 27 x+45=32 x+30 \Rightarrow 5 x=15 \Rightarrow x=3$. ∴ Greater number $=16 \times 3=48$.
Explanation as extracted from the printed page; notation may be imperfect.