Shortcut Trick Ratio of Mohan to Rakesh (Present) = 3 : 1 (Difference = 2) Ratio of Mohan to Rakesh (4 years ago) = 4 : 1 (Difference = 3) Equalize difference: Present (3:1)×3 = 9:3 | 4 yrs ago (4:1)×2 = 8:2 Ratio gap (9−8 or 3−2) = 1 unit → 4 years Rakesh present age = 3 units = 12 years Rakesh age after 7 years = 12 + 7 = 19 years ∴ The correct answer is 19 years. Alternate Method Given: Present age ratio Mohan:Rakesh = 3:1. Time interval = 4 years. Age after 7 years required. ⇒ Let Rakesh’s present age be x years. ⇒ Mohan’s present age = 3x years. ⇒ 4 years ago, Mohan’s age = 3x − 4 and Rakesh’s age = x − 4. ⇒ According to question: 3x − 4 = 4 × (x − 4) ⇒ 3x − 4 = 4x − 16 ⇒ 4x − 3x = 16 − 4 ⇒ x = 12 (Rakesh’s present age) ⇒ Age after 7 years = 12 + 7 = 19 years. ∴ The correct answer is 19 years. Related Concepts: Ratio Difference Equality When the age of two people changes over time, the absolute difference between their ages always remains constant. Age after 'n' years If present age is P, then age after n years is P + n and age n years ago was P − n. Cross-Multiplication Method For two ratios a:b and c:d with a change 'k', the value of 1 unit = |(b×c − a×d)| / |k×(c − d)|.