Question

5. The average age of 4 sisters is 20. If the ages of
3 sisters are 16 yr, 18 yr and 20 yr, the age of
the fourth sister is.​

Answer 1

Given

• The average age of 4 sisters is 20
• Ages of 3 sisters are 16 years, 18 years and 20 years

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To Find

• The age of 4th sister.

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Solution

Let's consider the age of the 4th sister as 'x'.

Formula to find Average ⇒ $\dfrac{Sum \ of \ all \ observations }{No.\ of \ observations }$

Average age ⇒ 20

Let's solve the following equation step-by-step to find the age of 4th sister.

$\dfrac{16+18+20+x}{4} = 20$

Step 1: Simplify the equation.

⇒ $\dfrac{16+18+20+x}{4} = 20$

⇒ $\dfrac{54+x}{4} = 20$

Step 2: Cross multiply.

⇒ $54+x = 20\times 4$

⇒ $54 +x = 80$

Step 3: Subtract 54 from both sides of the equation.

⇒ $54 +x - 54= 80 - 54$

⇒ $x = 26$

Let's verify if the age of the 4th sister is 26 years.

⇒  $\dfrac{16+18+20+26}{4} = 20$

⇒ $\dfrac{80}{4} = 20$

⇒ $20 =20$

∴ LHS = RHS

∴ The age of the 4th sister is 26 years.

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Answer 2

Answer:

Given :-

• The average age of 4 sister is 20. If the ages of 3 sisters and 16 yrs, 18 yrs and 20 yrs respectively.

To Find :-

• What is the age of fourth sister.

Solution :-

Let, the fourth sister age be x years.

According to the question,

⇒ $\sf \dfrac{16 + 18 + 20 + x}{4} =\: 20$

By doing cross multiplication we get,

⇒ $\sf 16 + 18 + 20 + x = 4(20)$

⇒ $\sf 34 + 20 + x =\: 4 \times 20$

⇒ $\sf 54 + x =\: 80$

⇒ $\sf x =\: 80 - 54$

➠ $\sf\bold{\red{x =\: 26\: years}}$

$\therefore$ The age of fourth sister is 26 years .

${\purple{\boxed{\large{\bold{VERIFICATION :-}}}}}$

↦ $\sf \dfrac{16 + 18 + 20 + x}{4} =\: 20$

By putting x = 26 we get,

↦ $\sf \dfrac{16 + 18 + 20 + 26}{4} =\: 20$

By doing cross multiplication we get,

↦ $\sf 16 + 18 + 20 + 26 =\: 4(20)$

↦ $\sf 34 + 46 =\: 4 \times 20$

↦ $\sf\bold{\green{80 =\: 80}}$

➦ LHS = RHS

Hence, Verified ✔