Eight years ago, the ratio of the ages of Samir and Varun was 4:3. Eight years hence, the ratio of their ag
6:5. What is the

1 thought on “Eight years ago, the ratio of the ages of Samir and Varun was 4:3. Eight years hence, the ratio of their ag<br />6:5. What is the”

1. GIVEN :-

   • Eight years ago, the ratio of the ages of Samir and Varun was 4:3.
   • Eight years hence, the ratio of their age 6:5.

   [tex] \\ [/tex]

   TO FIND :-

   • Sum of their present ages.

   [tex] \\ [/tex]

   SOLUTION :-

   Let present age of Samir be ‘x’yrs and Varun be ‘y’yrs.

   CASE 1 —

   Eight years ago, the ratio of the ages of Samir and Varun was 4:3.

   Eight years ago,

   • Age of Samir → ‘x – 8’ yrs
   • Age of Varun → ‘y – 8’ yrs
   • Ratio was 4:3.

   [tex] \\ \sf \: \dfrac{x – 8}{y – 8} = \dfrac{4}{3} \\ \\ \sf \: 3(x – 8) = 4(y – 8) \\ \\ \sf \: 3x – 24 = 4y – 32 \\ \\ \sf \: 3x – 4y = – 32 + 24 \\ \\ \sf \: 3x – 4y = – 8 \\ [/tex]

   Multiplying whole equation by 5,

   [tex] \\ \sf \: 15x – 20y = – 40 \: \: \: \: \: \: \: – – – (1) \\ \\ [/tex]

   CASE 2—

   Eight years hence, the ratio of their age 6:5.

   Eight years hence ,

   • Age of Samir → ‘x + 8’ yrs
   • Age of Varun → ‘y + 8’ yrs
   • Ratio will be 6:5.

   [tex] \\ \sf \: \dfrac{x + 8}{y + 8} = \dfrac{6}{5} \\ \\ \sf \: 5(x + 8) = 6(y + 8) \\ \\ \sf \: 5x + 40 = 6y + 48 \\ \\ \sf \: 5x – 6y = 48 – 40 \\ \\ \sf \: 5x – 6y = 8 \\ [/tex]

   Multiplying whole equation by 3,

   [tex] \\ \sf \: 15x – 18y = 24 \: \: \: \: \: \: \: – – – (3) \\ \\ [/tex]

   Subtracting equation (2) by equation (1) ,

   → 15x – 20y – (15x – 18y) = -40 – (24)

   → 15x – 20y – 15x + 18y = -40 – 24

   → -2y = -64

   → y = -64/-2

   → y = 32

   Putting y=32 in equation (3) ,

   → 15x – 18(32) = 24

   → 15x – 576 = 24

   → 15x = 24 + 576

   → 15x = 600

   → x = 600/15

   → x = 40

   Hence , age of Samir is 40 years and age of Varun is 32years.

   Sum of their ages = 40 + 32 = 72years.

   Hence , sum of the ages of Samir and Varun is 72 years.

   Reply