the sum of raju's age and half of sameer's age is 4 one third raju's age added to twice sameer's age is 5 find the sum of their ages
Answers
Given :
• Sum of Raju's age and half of Sameer's age = 4
• One third of Raju's age added to twice Sameer's age = 5
To find :
• Sum of their ages
Solution :
Let us assume the present age of Raju and Sameer be x and y respectively.
According to the first condition given in the question,
→ Sum of Raju's age and half of Sameer's age = 4
→ x + ½ × y = 4
→ x + y/2 = 4
→ (2x + y)/2 = 4
→ 2x + y = 8 -----(1)
According to the second condition given in the question,
→ One third of Raju's age added to twice Sameer's age = 5
→ ⅓ × x + 2 × y = 5
→ x/3 + 2y = 5
→ (x + 6y)/3 = 5
→ x + 6y = 15 -----(2)
Solve (1) and (2) :-
→ (2x + y = 8) × 1
→ 2x + y = 8 -------(3)
→ (x + 6y = 15) × 2
→ 2x + 12y = 30 -----(4)
Solving (3) and (4) :-
→ 2x + y = 8
→ 2x + 12y = 30
⠀(-)⠀(-)⠀⠀⠀(-)
______________
⠀⠀⠀- 11y = - 22
______________
→ - 11y = - 22
→ 11y = 22
→ y = 22/11
→ y = 2
The value of y = 2
Substitute the value of y in equation (1) :-
→ 2x + y = 8
→ 2x + 2 = 8
→ 2x = 8 - 2
→ 2x = 6
→ x = 6/2
→ x = 3
The value of x = 3
Therefore, the age of Raju and Sameer are :-
- Age of Raju = x = 3 years
- Age of Sameer = y = 2 years
Let us assume the present age of Raju and Sameer be x and y respectively.
According to the first condition given in the question,
→ Sum of Raju's age and half of Sameer's age = 4
→ x + ½ × y = 4
→ x + y/2 = 4
→ (2x + y)/2 = 4
→ 2x + y = 8 -----(1)
According to the second condition given in the question,
→ One third of Raju's age added to twice Sameer's age = 5
→ ⅓ × x + 2 × y = 5
→ x/3 + 2y = 5
→ (x + 6y)/3 = 5
→ x + 6y = 15 -----(2)
Solve (1) and (2) :-
→ (2x + y = 8) × 1
→ 2x + y = 8 -------(3)
→ (x + 6y = 15) × 2
→ 2x + 12y = 30 -----(4)
Solving (3) and (4) :-
→ 2x + y = 8
→ 2x + 12y = 30
⠀(-)⠀(-)⠀⠀⠀(-)
______________
⠀⠀⠀- 11y = - 22
______________
→ - 11y = - 22
→ 11y = 22
→ y = 22/11
→ y = 2
The value of y = 2
Substitute the value of y in equation (1) :-
→ 2x + y = 8
→ 2x + 2 = 8
→ 2x = 8 - 2
→ 2x = 6
→ x = 6/2
→ x = 3
The value of x = 3
Therefore, the age of Raju and Sameer are :-
- Age of Raju = x = 3 years
- Age of Sameer = y = 2 years
Sum of their ages = 3+2
= 5