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
Given :
• Five years ago, Anu was thrice as old as Sonu.
• After ten years, Anu will be twice as old as Sonu.
To find :
• Present age of Anu and Sonu
Solution :
Let,
- Present age of Anu = x years
- Present age Sonu = y years
Their ages 5 years ago :-
→ Age of Anu = x - 5 years
→ Age of Sonu = y - 5 years
According to the first condition given,
→ Age of Anu = 3(Age of Sonu)
→ x - 5 = 3(y - 5)
→ x - 5 = 3y - 15
→ x - 3y = - 15 + 5
→ x - 3y = - 10 ------(1)
Their ages after 10 years :-
→ Age of Anu = x + 10 years
→ Age of Sonu = y + 10 years
According to the second condition,
→ Age of Anu = 2(Age of Sonu)
→ x + 10 = 2(y + 10)
→ x + 10 = 2y + 20
→ x - 2y = 20 - 10
→ x - 2y = 10 ----------(2)
Solving (1) and (2) :-
→ x - 3y = - 10
→ x - 2y = 10
(-)⠀(+) ⠀(-)
___________
→ - y = - 20
___________
→ - y = - 20
→ y = 20
Substitute the value of y in equation (1) :-
→ x - 3y = - 10
→ x - 3(20) = - 10
→ x - 60 = - 10
→ x = - 10 + 60
→ x = 50
→ Present age of Anu = x = 50 years
→ Present age of Sonu = y = 20 years
Answer:
Anu's age is 50 and Sonu's age is 20
Step-by-step explanation:
Let the present age of
Anu be = x
Sonu be = y
Step 1 -
x-5 = 3(y-5) [substracted five as five years ago]
x-5 = 3y-15 [opening bracket]
x = 3y-15+5 [transposing 5 to RHS and changing - to +]
x = 3y-10 [value of x]
Step 2 -
x+10 = 2(y+10) [added 10 as after ten years]
x+10 = 2y+20 [opening bracket]
3y-10+10 = 2y+20 [adding value of x as per step 1]
3y-2y = 20 [transposing 2y to LHS and changing + to -]
y = 20 [value of y and age of Sonu]
Step 3 -
x = (3×20)-10 [using the value of x and y]
x = 60-10
x = 50 [Age of Anu]
Hence, Anu is 50 years old and Sonu is 20 years old.