Question

One year ago the ratio of Anil’s and Sunil’s age was 6:7. Four years hence their ratio would become 7:8. How old is Sunil?
A. 36
B. 26
C. 46
D. 40

Answer 1

Hint:Find the relation connecting the age of Anil and Sunil one year ago. Similarly find the relation connecting their age after 4 years. Thus solve by substituting the values.

Complete step-by-step answer:
Let us assume the age of Anil as ‘x’. Similarly let us assume the age of Sunil as ‘y’.
It is said that the ratio of their age one year ago was 6:7, i.e. x:y = 6:7.
Thus we can write it as,
\[\dfrac{x}{y}=\dfrac{6}{7}\]
\[\therefore x=\dfrac{6y}{7}\].
Thus we got a relation connecting the ages of Anil and Sunil one year ago.
Now it is said that after 4 years the ratio of their ages becomes 7:8.
Thus their age after 4 years is, \[=\left( x+1+4 \right):\left( y+1+4 \right)=x+5:y+5\].
The ratio of Anil and Sunil after four years is 7:8.
\[\Rightarrow x+5:y+5=7:8\].
We can write the above expression as,
\[\dfrac{x+5}{y+5}=\dfrac{7}{8}\]
Cross multiply and put \[x={}^{6y}/{}_{7}\].
$\Rightarrow 8\left( x+5 \right)=7(y+5)$
 $\Rightarrow 8\left[ \dfrac{6y}{7}+5 \right]=7y+35$
$\Rightarrow\dfrac{48y}{7}+40=7y+35 $
$\Rightarrow 48y+280=49y+245 $
$\Rightarrow 49y-48y=280-215 $
 $ y=35. $
Now let us get x, put y = 35.
\[x=\dfrac{6\times 35}{7}=6\times 5=30\].
Thus we get the age of Anil and Sunil one year ago as 30 and 35.
Thus the present age of Anil = x + 1 = 30 + 1 = 31.
Present age of Sunil = y + 1 = 35 + 1 =36.
Thus Sunil is 36 years old.
Option A is the correct answer.

Note: We can also take the ratio of age of Anil and Sunil as 6x : 7x.
Thus after 5 years, i.e. (present age + 4 years), their age becomes 6x + 5 : 7x + 5 which is 7:8.
\[\therefore \dfrac{6x+5}{7x+5}=\dfrac{7}{8}\]
Cross multiply and we get x = 5.
Sunil’s present age = 7x + 1 = \[7\times 5+1\] = 36 years.