Practice Questions
The present age of a father is four times that of his son. After 8 years, he will be three times the son’s age. Find their present ages.
Let son = $x$, father = $4x$. $(4x+8) = 3(x+8) \Rightarrow 4x+8 = 3x+24 \Rightarrow x=16$. Father = $4 \times 16 = 64$, son = 16.
The sum of ages of A and B is 48. Five years ago, the ratio of their ages was 5:3. Find present ages.
Let ages 5 years ago be $5x$ and $3x$. Sum of ages 5 years ago = $48 - 10 = 38$. $8x = 38 \Rightarrow x = 4.75$. Ages 5 years ago: 23.75, 14.25. Present ages: 28.75, 19.25.
A is 10 years older than B. After 6 years, A's age will be twice B's age. Find their present ages.
$A = B + 10$. $(A+6) = 2(B+6) \Rightarrow (B+10+6) = 2B+12 \Rightarrow B+16 = 2B+12 \Rightarrow B=4$. So A=14, B=4.
The present ages of mother and daughter are in ratio 7:2. After 5 years, ratio becomes 9:4. Find present ages.
$(7x+5)/(2x+5) = 9/4 \Rightarrow 28x+20 = 18x+45 \Rightarrow 10x=25 \Rightarrow x=2.5$. Ages: 17.5, 5.
Ten years hence, the ratio of ages of A and B will be 4:5. Ten years ago it was 2:3. Find present ages.
$(x-10)/(y-10) = 2/3$ and $(x+10)/(y+10) = 4/5$. Solving gives $x=30, y=40$.
The average age of a family of 4 members is 25 years. If the youngest is 5 years old, find the average age of the family at the time of the birth of the youngest member.
Current sum = $4 \times 25 = 100$. 5 years ago, total sum = $100 - (4 \times 5) = 80$. Average of 3 members = $80/3 = 26.67$.
The ratio of ages of Ram and Shyam is 5:4. After 10 years, the ratio becomes 7:6. Find the present age of Ram.
Let ages be $5x$ and $4x$. $(5x+10)/(4x+10) = 7/6 \Rightarrow 30x+60 = 28x+70 \Rightarrow 2x=10 \Rightarrow x=5$. Ram = $5 \times 5 = 25$.
A mother is 30 years older than her daughter. After 8 years, the mother's age will be twice the daughter's age. Find the daughter's present age.
Let daughter = $x$, mother = $x+30$. $(x+30+8) = 2(x+8) \Rightarrow x+38 = 2x+16 \Rightarrow x = 22$.
Six years ago, the ratio of ages of P and Q was 6:5. Four years hence, it will be 11:10. Find P's present age.
Let ages 6 years ago be $6x$ and $5x$. Present ages: $6x+6$, $5x+6$. After 4 more years: $(6x+10)/(5x+10) = 11/10 \Rightarrow 60x+100 = 55x+110 \Rightarrow 5x=10 \Rightarrow x=2$. P = $6 \times 2 + 6 = 18$.
The sum of ages of father and son is 50. Five years ago, the father was 5 times as old as the son. Find their present ages.
Let son = $x$, father = $50-x$. Five years ago: $(50-x-5) = 5(x-5) \Rightarrow 45-x = 5x-25 \Rightarrow 6x=70 \Rightarrow x=10$. Father = 40, son = 10.
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