Question

20. The ages of Sonal and Manoj are in the ratio 7:5. Ten years hence, the ratio of their ages
will be 9: 7. Find their present ages.
21. Five years ago a man was seven times as old as his son. Five years hence, the father will be
three times as old as his son. Find their present ages.​

Answer 1

20 .

Given :

 The ages of Sonal and Manoj are in the ratio 7:5 .Ten years hence, the ratio of their ages  will be 9: 7

To Find :

Present ages

Solution :

Let present age of Sonal and Manoj be 7x , 5x

Ten years hence, the ratio of their ages  will be 9: 7

$\to \sf \dfrac{7x+10}{5x+10}=\dfrac{9}{7}\\\\\to \sf 7(7x+10)=9(5x+10)\\\\\to \sf 49x+70=45x+90\\\\\to \sf 49x-45x=90-70\\\\\to \sf 4x=20\\\\\to \sf x=5\ \; \bigstar$

Present age of Sonal , 7x = 35 years  $\orange{\bigstar}$

Present age of Manoj , 5x = 25 years  $\green{\bigstar}$

______________________________________

21 .

Given :

Five years ago a man was seven times as old as his son. Five years hence, the father will be  three times as old as his son

To Find :

Present ages

Solution :

Five years ago ,

Let age of son be x

Age of man = 7x

Five years hence, the father will be  three times as old as his son

$\to \sf 7x+10=3(x+10)\\\to \sf 7x+10=3x+30\\\to \sf 7x-3x=30-10\\\to \sf 4x=20\\\to \sf x=5\ \; \bigstar$

Present age of son , x + 5 = 10 years  $\blue{\bigstar}$

Present age of Father , 7x + 5 = 40 years  $\red{\bigstar}$

Or

Alternate Method :

Let present age of father be x

Present age of son be y

Five years ago ,

Father's age = x - 5

Son's age = y - 5

Five years ago a man was seven times as old as his son

$\to \sf (x-5)=7(y-5)\\\to \sf x-5=7y-35\\\to \sf x-7y=-30...(1)$

After 5 years ,

Father's age = x + 5

Son's age = y + 5

Five years hence, the father will be  three times as old as his son

$\to \sf (x+5)=3(y+5)\\\to \sf x+5=3y+15\\\sf \to x-3y=10...(2)$

Solve (2) - (1) ,

$\to \sf (x-3y)-(x-7y)=10-(-30)\\\to \sf x-3y-x+7y=10+30\\\to \sf 4y=40\\\to \sf y=10\ \; \bigstar$

Sub. y value in (2) ,

$\to \sf x-3(10)=10\\\to \sf x-30=10\\\to \sf x=10+30\\\to \sf x=40\ \; \bigstar$

Present age of father , x = 40 years  $\purple{\bigstar}$

Present age of son , y = 10 years  $\pink{\bigstar}$