The sum of the present ages of Ram and Shyam is 75 years. Ten years ago, Ram's age was 4 times the age of Shyam. Find the difference between their present ages (in years).
Answers
Answer:
33 years
Step-by-step explanation:
Let's take Ram's age as "x" and Shyam's age as "y"
we know that,
x+y = 75 (eq 1)
10 years ago
==> x-10 = 4(y-10)
==> x-10 = 4y -40
==> 30 = 4y-x
==> 30 = 4y -(75-y) {by using eq 1}
==> 30 = 4y-75+y
==> 105 = 5y
==> y = 21
In eq 1
x = 75-21
==> 54
So the difference between their present ages is 54-21 = 33 years
Given information,
The sum of the present ages of Ram and Shyam is 75 years. Ten years ago, Ram's age was 4 times the age of Shyam. Find the difference between their present ages (in years).
- Sum of present ages of Ram and Shyam = 75 years
- Ten years ago, Ram's age was 4 times the age of Shyam.
- Difference b/w their ages = ?
Let,
- Present age of Ram = x years
- Present age of Shyam = y years
- Also, as sum of their ages is 75. So, present age of Ram = (75 - y) years [x = 75 - y] – (1)
- Ram age, 10 years ago = (x - 10) years
- Shyam age, 10 years ago = (y - 10) years
According to the Question,
- Ten years ago, Ram's age was 4 times the age of Shyam.
Therefore,
➻ Ram's age = 4(Shyam's age)
➻ x - 10 = 4(y - 10)
➻ x - 10 = 4y - 40
From (1) putting in above eqⁿ,
➻ (75 - y) - 10 = 4y - 40
➻ 75 - y - 10 = 4y - 40
➻ 75 - 10 - y = 4y - 40
➻ 65 - y = 4y - 40
➻ 65 + 40 = 4y + y
➻ 105 = 5y
➻ 5y = 105
➻ y = 105/5
➻ y = 21
- Hence, present age of Shyam (y) is 21 years.
Now,
➻ x = 75 - y⠀⠀⠀⠀⠀⠀⠀⠀ [From (1)]
Putting value of y,
➻ x = 75 - 21
➻ x = 54
- Hence, present age of Ram (x) is 54 years.
Now,
➻ Difference b/w their ages = 54 - 21
➻ Difference b/w their ages = 33
- Hence, difference between their present ages is 33 years.
Verification,
- Ten years ago, Ram's age was 4 times the age of Shyam.
Therefore,
➻ Ram's age = 4(Shyam's age)
➻ x - 10 = 4(y - 10)
Putting value of x and y,
➻ 54 - 10 = 4(21 - 10)
➻ 44 = 4(11)
➻ 44 = 4 × 11
➻ 44 = 44
➻ LHS = RHS
- Hence, Verified ✔