Advertisements
Advertisements
Question
Father's age is three times the sum of age of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.
Solution
Let the present age of father be x years and the present age of his son be y years.
The present age of father is three times the age of the son. Thus, we have
`x= 3y`
`⇒ x - 3y =0`
After 12 years, father’s age will be (x + 12) years and son’s age will be (y + 12) years. Thus using the given information, we have
`x+ 12 = 2(y+12)`
`⇒ x + 12 = 2y +24`
`⇒ x - 2y -12 =0`
So, we have two equations
`x- 3y =0`
`x-2y -12=0`
Here x and y are unknowns. We have to solve the above equations for x and y.
By using cross-multiplication, we have
`x/((-3)xx(-12)-(-2)xx0)=(-y)/((1xx(-12)-1xx0))=1/((1xx(-2)-1xx(-3)))`
`⇒ x/(36-0)=(-y)/(-12-0)=1/(-2+3)`
`⇒ x/(36)= (-y)/-12=1/1`
`⇒ x/36=y/12=1`
`⇒ x = 36, y=12`
Hence, the present age of father is 36 years and the present age of son is 12 years.
APPEARS IN
RELATED QUESTIONS
Solve `\frac { 2 }{ x } + \frac { 1 }{ 3y } = \frac { 1}{ 5 }; \frac { 3 }{ x } + \frac { 2 }{ 3y } = 2` and also find ‘a’ for which y = ax – 2
One says, "Give me a hundred, friend! I shall then become twice as rich as you". The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II)
[Hint: x + 100 = 2 (y − 100), y + 10 = 6(x − 10)]
ABCD is a cyclic quadrilateral finds the angles of the cyclic quadrilateral.
A and B each have a certain number of mangoes. A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you." B replies, "if you give me 10, I will have thrice as many as left with you." How many mangoes does each have?
The sum of two numbers is 8. If their sum is four times their difference, find the numbers.
The sum of two numbers is 1000 and the difference between their squares is 256000. Find the numbers.
A fraction becomes 1/3 if 1 is subtracted from both its numerator and denominator. It 1 is added to both the numerator and denominator, it becomes 1/2. Find the fraction.
The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. Find the fraction.
State with reason whether the point (3, −2) will lie on the graph of the equation 5m – 3n = − 21
Asha has only ₹1 and ₹2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is ₹75, then the number of ₹1 and ₹2 coins are, respectively.
