Q7. Five years ago, Anu was thrice as old as Sonu. After ten years, Anu will be
twice as old as Sonu. How old are Anu and Sonu?
Answers
Answer:
Anu = 50 yrs.
Sonu = 20 yrs.
Step-by-step explanation:
Let the present ages of Anu and Sonu are x and y yrs. respectively.
Fice years ago.
Age of Anu = (x-5) yrs.
Age of Sonu = (y-5) yrs.
But, Anu was thrice as old as Sonu.
Therefore, we will get,
=> x - 5 = 3(y-5)
=> x -5 = 3y - 15
=> x - 3y - 5 + 15 = 0
=> x - 3y + 10 = 0 .......(1)
After ten years,
Age of Anu = (x+10) yrs.
Age of Sonu = (y+10) yrs.
But, Anu will be twice as old as Sonu.
Therefore, we will get,
=> x + 10 = 2(y+10)
=> x + 10 = 2y + 20
=> x - 2y + 10 - 20 = 0
=> x - 2y - 10 = 0 .........(2)
Substracting eqn (2) from (1), we get,
=> -3y -(-2y) +10 - (-10) = 0
=> -3y + 2y + 10 + 10 = 0
=> -y + 20 = 0
=> y = 20
Putting this value in (1), we get,
=> x - 3(20) + 10 = 0
=> x - 60 + 10 = 0
=> x - 50 = 0
=> x = 50
Hence, present ages of Anu and Sonu are 50 yrs. and 20 yrs. respectively.
Concept:
Linear equation are the equation which contains one or more variables whose maximum degree is 1.
Linear equation in two variables can be solved in multiple ways:
Substitution method:One variable is written in the for of other.
Elimination method: ONe variable is eliminated by addition , subtraction or multiplication of some constant
Cross multiplication: By using cramer's rule
Given:
Five years ago, Anu was thrice as old as Sonu. After ten years, Anu will be
twice as old as Sonu.
FIND:
Age of Sonu and Anu
SOLUTION:
Let the age of Anu be x years and Sonu be y years.
5 Years Ago,
Age of Anu = x - 5 years
Age of Sonu = y - 5 years
Given ,
( x - 5) = 3(y-5)
=> x = 3y - 15 + 5
x = 3y - 10 ---------------------------(1)
Ten Years Later,
Age of Anu = x + 10 years
Age of Sonu = y + 10 years
Given ,
( x + 10) = 2(y + 10)
=> 3y - 10 + 10 = 2y + 20
=> 3y - 2y = 20
=> y = 20
Substituting ( y = 20) in eq(1).
=> x = 3y - 10
=> x = 60 - 10
=> x = 50
Hence, Anu's age = x = 50 years
Sonu's age = y = 20 years
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