Pramod is 15 years younger than his sister after 5 years he will be half his sister age find the present age
P = Pramod age
S = Sister age
Difference of their age now = 15 yr
So :
P = S - 15
After 5 years Pramod will be 5 years older, and sister will be 5 years older.
Ratio of their age will be :
( P + 5 ) / ( S + 5 ) = 1 / 2
P = S - 15 so :
( S - 15 + 5) / ( S + 5 ) = 1 / 2
( S - 10 ) / ( S + 5 ) = 1 / 2
Now you must solve equation :
( S - 10 ) / ( S + 5 ) = 1 / 2 Multiply both sides by 2
2 ( S - 10 ) / ( S + 5 ) = 1
( 2 S - 20 ) / ( S + 5 ) = 1 Multiply both sides by S + 5
2 S - 20 = S + 5 Subtract S to both sides
2 S - 20 - S = S + 5 - S
S - 20 = 5 Add 20 to both sides
S - 20 + 20 = 5 + 20
S = 25
P = S - 15 = 10
The present age :
Pramod 10 yr
Sister 25 yr
Proof :
After 5 years Pramod will be 10 + 5 = 15 yr old.
Sister will be 25 + 5 = 30 yr old.
15 / 30 = 1 / 2
Let's set up the equation to solve this problem.
Let X be Pramod's present age and Y be his sister's present age.
According to the problem, Pramod is currently 15 years younger than his sister, so we can write the equation:
X = Y - 15
After 5 years, Pramod's age will be X + 5 and his sister's age will be Y + 5. We also know that after 5 years, Pramod's age will be half his sister's age, so we can write the equation:
X + 5 = 1/2 * (Y + 5)
Now we have a system of equations:
X = Y - 15
X + 5 = 1/2 * (Y + 5)
We can substitute the value of X from the first equation into the second equation:
(Y - 15) + 5 = 1/2 * (Y + 5)
Simplifying, we get:
Y - 10 = 1/2 * Y + 5/2
Multiply both sides of the equation by 2 to eliminate the fraction:
2(Y - 10) = Y + 5
Expand and simplify:
2Y - 20 = Y + 5
Subtract Y from both sides of the equation:
2Y - Y - 20 = 5
Simplify:
Y - 20 = 5
Add 20 to both sides of the equation:
Y = 25
Now we can substitute this value back into the first equation to find X:
X = Y - 15
X = 25 - 15
X = 10
Therefore, Pramod is currently 10 years old and his sister is currently 25 years old.
To find Pramod's present age, we can create an equation based on the given information.
Let's assume Pramod's present age is represented by P and his sister's present age is represented by S.
According to the given information, "Pramod is 15 years younger than his sister." This can be translated into the equation: P = S - 15.
The second piece of information states, "After 5 years, he will be half his sister's age." After 5 years, Pramod will be P + 5 years old, and his sister will be S + 5 years old. This leads to the equation: P + 5 = (S + 5) / 2.
Now, we can set up a system of equations using both equations we derived:
1) P = S - 15
2) P + 5 = (S + 5) / 2
To solve this system of equations, we can substitute the value of P from equation 1 into equation 2:
S - 15 + 5 = (S + 5) / 2
S - 10 = (S + 5) / 2
Cross-multiplying, we have:
2(S - 10) = S + 5
2S - 20 = S + 5
2S - S = 5 + 20
S = 25
Now that we know the sister's present age, we can substitute this value back into equation 1 to find Pramod's present age:
P = S - 15
P = 25 - 15
P = 10
Therefore, Pramod's present age is 10 years old and his sister's present age is 25 years old.