Question

A man leaves $\frac{1}{2}$ of his property to his wife, $\frac{1}{3}$to his son and the remaining to his daughter. If the daughter’s share is ₹ 5,000, how much money did the man leave? How much money did his wife get? What is his son’s share?

Chapter- Linear Equation​
Class- VIII

Answer 1

Let,

• The share of the man be $\sf'x'$

According to the given,

• Wife's share would be $\sf{{\dfrac{1}{2}}x}$ of his property $\sf---(1)$
• Son's share would be $\sf{{\dfrac{1}{3}}x}$ of his property $\sf---(2)$
• Daughter = $\sf{Rs.\:5000}$

And we could proclaim that sum of $\sf{\dfrac{1}{2}}$ of $\sf{x}$ and $\sf{\dfrac{1}{3}}$ of $\sf{x}$ subtract from $\sf{x}$ (man's share) which will be equal to Daughter's share of Rs. 5000.

Solving,

$\sf\implies{x\:-\:{\dfrac{1}{2}}x\:+\:{\dfrac{1}{3}}x\:=\:5000}$

$\sf\implies{x\:-\:{\dfrac{3x\:+\:2x}{6}}\:=\:5000}$

$\sf\implies{x\:-\:{\dfrac{5x}{6}}\:=\:5000}$

$\sf\implies{{\dfrac{6x\:-\:5x}{6}}\:=\:5000}$

$\sf\implies{{\dfrac{x}{6}}\:=\:5000}$

$\sf\implies{x\:=\:5000\:\times\:6}$

$\sf\implies{x\:=\:30,000}$

The man's share is Rs. 30,000.

Substituting x value in (1), we get,

Wife's share = $\sf{{\dfrac{1}{2}}x}$

$\sf\implies{{\dfrac{1}{2}}x}$

$\sf\implies{{\dfrac{x}{2}}}$

$\sf\implies{{\dfrac{30000}{2}}}$

$\sf\implies{15,000}$

Substituting x value in (2), we get,

Son's share = $\sf{{\dfrac{1}{3}}x}$

$\sf\implies{{\dfrac{1}{3}}x}$

$\sf\implies{{\dfrac{x}{3}}}$

$\sf\implies{{\dfrac{30000}{3}}}$

$\sf\implies{10000}$

Hence,

• The man's share is Rs. 30,000,
• Wife's share is Rs. 15000,
• Son's share is Rs. 10000 and
• Daughter's share is Rs. 5000.

Answer 2

$☯ \: {\underline{\underline{\mathfrak\red{Question:-}}}}$

A man leavesb½ of his property to his wife, ⅓ to his son and the remaining to his daughter. If the daughter’s share is ₹ 5,000, how much money did the man leave? How much money did his wife get? What is his son’s share?

⠀⠀⠀⠀

$☯ \: {\underline{\underline{\mathfrak\red{Answer:-}}}}$

Let the total Money be ₹ x.

⠀⠀⠀⠀⠀⠀$\sf{Wife \: share = \frac{1}{2} \: of \: ₹ \: x }$⠀⠀

⠀⠀⠀⠀⠀⠀$\sf{:⇒\: \frac{1}{2} \: \times \: x }$⠀⠀

⠀⠀⠀⠀⠀⠀$\sf{:⇒\:₹ \: \frac{x}{2} }$

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀$\sf{Son \: share = \frac{1}{3} \: of \: ₹x}$

⠀⠀⠀⠀⠀⠀$\sf{ :⇒\:\frac{1}{3} \times x }$

⠀⠀⠀⠀⠀⠀$\sf{:⇒\: ₹ \: \frac{x}{3} }$

⠀⠀⠀⠀⠀⠀

⠀$\sf{Remaining \: = x - \frac{x}{2} - \frac{x}{3} }$⠀

⠀⠀⠀⠀⠀⠀$\sf{ :⇒\:₹ \frac{6x - 3x - 2x}{6} }$

⠀⠀⠀⠀⠀⠀$\sf{:⇒\:₹ \: \frac{3x - 2x}{6} }$⠀

⠀⠀⠀⠀⠀⠀$\sf{:⇒\:₹ \frac{x}{6} }$

⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀$\sf{Daughter \: share = ₹ \frac{x}{6} }$⠀⠀

⠀⠀⠀⠀⠀⠀$\sf{:⇒\: ₹ \: 5000 = \frac{x}{6} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀${\underline{\boxed{\bf{\pink{ :⇒\:₹ \: x = 35,000}}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀The man left ₹ 35,000

⠀

⠀⠀⠀⠀⠀$\sf{Wife \: share = \frac{\:₹ \: 35000}{2} }$

⠀⠀⠀⠀⠀⠀${\underline{\boxed{\bf{\green{ :⇒\:₹ \: x = 17500}}}}}$

⠀

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀$\sf{son \: share = \frac{\:₹ \: 35000}{3} }$

⠀⠀⠀⠀⠀⠀${\underline{\boxed{\bf{\green{:⇒ \:₹ \: x = 11666.6}}}}}$

⠀⠀⠀

⠀⠀

Hence,⠀⠀⠀

• The man share is Rs. 35,000,
• Wife share is Rs. 17500,
• Son share is Rs. 11666.6 and
• Daughters share is Rs, 35,000

⠀⠀⠀

⠀⠀⠀

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