Question

the difference of the age of two sister is 5 yrs and the product of their age is 24 find the age of the two sister

Answer 1

Answer:

Let the sister and her sister's age be X yrs and X+5 yrs respectively.

As per the question,

X(X+5)=104

X

2

+5X−104=0

X

2

+13X−8X+132=0

X(X+13)−8(X+13)=0

(X+13)(X—8)=0

∴X=8orX=−13

∴ the ages of sisters are 8 years & 8+5=13 years respectively, as the age can't be negative.

Answer 2

Answer:

《☆》Question -:

☆》The difference of the age of two sister is 5 yrs and the product of their age is 24. Find the age of the two sister.

《☆》Given -:

• Difference of age of both sisters = 5.
• And, the product if their ages = 24.

《☆》To Find -:

• Age of both sisters.

《☆》Solution -:

Let,

• The age of first girl be X.
• and, the age of second girl be Y.

According to the question,

• Difference of ages of both girls (X - Y)= 5. $\Longrightarrow \red{Eq. 1.}$

And,

• Product of their ages [X × Y] = 24.$\Longrightarrow\red{Eq. 2.}$

➡From Eq. 1, we get,

• X - Y = 5.
• $\boxed {X = 5 + y.} \Longrightarrow \blue {Eq.3.}$

➡By Putting the value of X from Eq.3 in Eq.2, we get,

${X × Y = 24.} \\ {(5 + Y)Y = 24.} \\ {5Y + Y^2 = 24} \\ {Y^2 + 5Y - 24 = 0.} \\ \\ \textsf{Now, We will use the splitting of middle term method for finding the ages.} \\ \\ {Y^2 + 5Y - 24 = 0.} \\ {Y^2 + (8-3)Y - 24 = 0.} \\ {Y^2 + 8Y - 3y - 24 = 0.} \\ {Y(Y + 8) - 3 (Y + 8) = 0.} \\ {(Y - 3)(Y + 8) = 0.} \\ \boxed { Y = 3.}*$ $\\ \textsf{By putting the value of Y in Eq.3, we get,}$

${X = 5 + 3} \\ \boxed {X = 8.}*$

《☆》Answer -:

• Hence, Age of first girl ( X ) = 8.
• Age of second girl (Y) = 3.

**Ages could not be negative, So,we have not taken.

** Values of X and Y may interchange .