The age of a father is equal to the sum of the ages of his four children. After 20 years, the sum of the ages of the children will be twice the age of the father. Find the age of the father.
Step-by-step solution
Idea: Let the father be x years and the children’s total y years. In 20 years each of the four children gains 20 years, so their total gains 4 × 20 = 80.
- Now: x = y … (1).½ mark
- After 20 years: father x + 20; children’s total y + 4 × 20 = y + 80. So y + 80 = 2(x + 20) ⇒ y − 2x = −40 … (2).1½ marks
- (1) in (2): x − 2x = −40 ⇒ x = 40. The father is 40 years old.1 mark
Check: Now: father 40, children’s total 40 ✓. In 20 years: father 60, children 40 + 80 = 120 = 2 × 60 ✓.
Answer to write in the exam
Let father = x years, sum of children’s ages = y years
x = y … (1)
y + 80 = 2(x + 20) … (2)
(1) in (2): x + 80 = 2x + 40 ⇒ x = 40
∴ Father’s age = 40 years
Common mistakes that cost marks
- Adding only 20 to the children’s total instead of 4 × 20 = 80.
- Writing 2(y + 80) = x + 20 (doubling the wrong side).
How this can come in the exam
A mother’s age equals the sum of her 3 children’s ages. In 15 years the children’s total will be 1½ times her age. Her present age is
- 30
- 45
- 60
- 36
Show answer
(B) 45
x + 45 = 1.5(x + 15) ⇒ 0.5x = 22.5 ⇒ x = 45.
Try one yourself
A man’s age equals the sum of the ages of his five children. After 12 years, the children’s total age will be twice his age. Find his age.
Show answer
x + 60 = 2(x + 12) ⇒ x = 36 years (check: 48 and 96 = 2 × 48).
More questions like this
- Radha stops at a fruit cart. The price tags say that mangoes cost ₹60 per kg and bananas cost ₹50 per kg. She buys some kilograms of mangoes and some kilograms of bananas. Altogether, she pays ₹280. Can we express this situation as an equation?
- Write each of the following equations in standard form, ax + by + c = 0, and indicate the values of a, b and c in each case:
- Write a linear equation in two variables in which a = 3, b = 0 and c = −15.
- Complete the following table after expressing the given linear equations in standard form.
Linear equation in two variables Standard Form Coefficient of x Coefficient of y Constant term y − 15 = √2x 3y − 2x = 0 5x = 3y x = 8 3y = 1 - (i) The cost of a notebook is twice the cost of a pen. Consider the cost of a notebook to be ₹t and that of a pen to be ₹p. Charlie wrote t = 2p, whereas Meera wrote p = 2t. Which of these two representations is correct?
(ii) In a one-day International Cricket match between India and Sri Lanka played in Nagpur, two Indian batsmen together scored 176 runs. Manisha expressed this situation as x + y = 176, where the number of runs scored by one batsman is x, and the number of runs scored by the other is y. Is this a correct representation?
All Linear equations in two variables questions · All maths questions