Question

The present ages of Ram, Rahim and Robert are
in proportion of 5:7:8. Six years ago, the sum of
their ages is 42. Find their present ages.
1. 20, 25, 30
2. 25, 35, 40
3. 20, 28, 32
4. 15, 21, 24​

Answer 1

• The present ages of Ram, Rahim and Robert are in proportion of 5:7:8

Let Present age of Ram, Rahim and Robert be 5x, 7x and 8x Respectively.

6 years ago,

• Ram's age be (5x - 6)
• Rahim's age be (7x - 6)
• Robert's age be (8x - 6)
• Sum of their ages is 42

$\ \circ \ {\pmb{\underline{\sf{ According \ to \ Question: }}}} \\ \\ \\ \colon\implies{\sf{ (5x-6)+(7x - 6)+(8x - 6) = 42 }} \\ \\ \\ \colon\implies{\sf{ 5x-6+7x-6+8x-6=42}} \\ \\ \\ \colon\implies{\sf{ 20x-18 = 42 }} \\ \\ \\ \colon\implies{\sf{ 20x = 42 + 18 }} \\ \\ \\ \colon\implies{\sf{ \cancel{20} x = \cancel{60} }} \\ \\ \\ \colon\implies{\sf{ x = 3}}$

Hence,

${ \bigstar }$ Putting values,

• Ram's age = 5x = 15 Years
• Rahim's age = 7x = 21 years
• Robert's age = 8x = 24 years