Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
When 1 is added to each of the two given numbers, their ratio becomes 3 : 4 and when 5 is subtracted from each, the ratio becomes 7 : 10. One of the numbers is
(a)11
(b)15
(c)26
(d)36
Answer
Answer (as printed): C
Explanation
Let the numbers be $x$ and $y$. Then, $\frac{x+1}{y+1}=\frac{3}{4}$ and $\frac{x-5}{y-5}=\frac{7}{10}$ $$\begin{aligned} & \Rightarrow 4 x+4=3 y+3 \text { and } 10 x-50=7 y-35 \\ & \Rightarrow 4 x-3 y=-1 \text { and } 10 x-7 y=15 \\ & \Rightarrow 20 x-15 y=-5 \end{aligned}$$ and $20 x-14 y=30$ Subtracting (i) from (ii), we get : $y=35$. Putting $y=35$ in (i), we get : $$20 x=520 \text { or } x=26 .$$
Explanation as extracted from the printed page; notation may be imperfect.