Solve the following problem
. The ages of Ramu and Somu are in the ratio 5:7 four years from now the ratio of
thei

2 thoughts on “<br />Solve the following problem<br />. The ages of Ramu and Somu are in the ratio 5:7 four years from now the ratio of<br />thei”

1. Answer:

   The Present Age of Ramu is 20 years

   The Present Age of Somu is 28 years

   Step-by-step explanation:

   Given,

   • The Ratio of Present Ages of Ramu and Somu is 5 : 7.

   After 4 years,

   • The Ratio of Their Ages becom 3 : 4.

   To Find,

   • The Present Ages of Ramu and Somu.

   Solution,

   Let’s,

   The Present Age of Ramu = 5X

   So,

   The Present Age of Somu = 7X

   After 4 years,

   The Age of Ramu = 5X + 4

   The Age of Somu = 7X + 4

   The Ratio of Their Ages After 4 years = 3 : 4

   → (5X + 4) : (7X + 4) = 3 : 4

   → (5X + 4)/(7X + 4) = 3/4

   → 4(5X + 4) = 3(7X + 4)

   → 4(5X) + 4(4) = 3(7X) + 3(4)

   → 20X + 16 = 21X + 12

   → 16 – 12 = X

   → X = 4

   The Present Age of Ramu = 5X

   → The Present Age of Ramu = 5(4)

   The Present Age of Ramu = 20 years

   The Present Age of Somu = 7X

   → The Present Age of Somu = 7(4)

   The Present Age of Somu = 28 years

   Required Answer,

   The Present Age of Ramu = 20 years

   The Present Age of Somu = 28 years

   Reply

2. Answer :–

   • Ramu’s age is 20 years.
   • Somu’s age is 28 years.

   Given :–

   • The ages of Ranu and Somu are in the ratio 5 : 7.
   • Four years from now, the ratio of their ages will be 3 : 4.

   To find :–

   • Their present ages.

   Step-by-step explanation :–

   • The ages of Ramu and Somu are in the ratio 5 : 7, so let their ages be 5x and 7x respectively.

   After four years,

   • Ramu’s age will be 5x + 4.
   • Somu’s age will be 7x + 4.

   It has been given that :–

   • After four years, the ages of Ramu and Somu will be in the ratio 3 : 4.

   ––––––––––––––

   [tex] \sf\dfrac{5x + 4}{7x + 4} = \dfrac{3}{4} [/tex]

   By cross multiplication,

   [tex] \sf4 \: (5x + 4) = 3 \: (7x + 4)[/tex]

   Removing the brackets,

   [tex] \sf20x + 16 = 21x + 12[/tex]

   Putting the constant and variable terms on different sides by the method of transposition,

   [tex] \sf20x – 21x = 12 – 16[/tex]

   On simplifying,

   [tex] \sf \cancel{-} x = \cancel{-} 4[/tex]

   Cutting off the negative sign,

   [tex] \underline{ \boxed{\sf x = 4}}[/tex]

   ————–

   Hence, their present ages are :–

   [tex] \rm Ramu’s \: age = 5x = 5 \times 4 = 20.[/tex]

   [tex] \rm Somu’s \: age = 7x = 7 \times 4 = 28.[/tex]

   Reply