Question

Present ages of Vatsala and Sara are 14 years and 10 years respectively. After how many years the ratio of their ages will becomes 5 : 4 ?

• A. $8$
• B. $6$
• C. $5.5$
• D. $4$

Answer 1

The correct option is B $6$

Present age of Vatsala $=14$ years

Present age of Sara $=10$ years

Let after $x$ years, ratio of their ages will become $5:4$

Age of Vatsala after $x$ years $=14+x$ years

Age of Sara after $x$ years $=10+x$ years

Now,

$\frac{14+x}{10+x}=\frac{5}{4}$

Cross multiply:

$4(14+x)=5(10+x)$

$56+4x=50+5x$

$56-50=5x-4x$

$6=x$

Therefore, after $6$ years, ratio of their ages will become $5:4$