UPTET Paper 1 Model Test 3

Concept:This is a problem on ages where ratios change over time. The difference between the ages of any two people always remains constant.Explanation:Let one year ago, A's age = $x$ and B's age = $2x$. Present age of A = $x + 1$, present age of B = $2x + 1$. After 9 years, A's age = $x + 10$, B's age = $2x + 10$. Given ratio after 9 years: $(2x + 10) : (x + 10) = 4 : 3$. Cross-multiply: $3(2x + 10) = 4(x + 10)$. Solve: $6x + 30 = 4x + 40$ → $2x = 10$ → $x = 5$. So present ages: A = $5 + 1 = 6$ years, B = $2 \times 5 + 1 = 11$ years. Sum of present ages = $6 + 11 = 17$ years.Shortcut:Ratio 1 year ago, B : A = 2 : 1. Ratio after 9 years, B : A = 4 : 3. Time gap between both ratios = $1 + 9 = 10$ years. Cross difference = $(2 \times 3) - (4 \times 1) = 6 - 4 = 2$ parts. These 2 parts equal 10 years. So 1 part = 5 years. Ages 1 year ago: A = 5 years, B = 10 years. Present ages: A = 5 + 1 = 6, B = 10 + 1 = 11. Sum = $6 + 11 = 17$ years.Answer:17 years