Question

If 1/4 of a number is added to 1/3of the number, the result is 15 greater than half of that number. Find the number.​

Answer 1

Answer :

• The number is 180

Given :

• If 1/4 of a number is added to 1/3 of the number
• The result is 15 greater than half of that number

To find :

• The number

Solution :

• Let the number be x

Given, if 1/4 of a number is added to 1/3 of the number so,

• x/4 + x/3

and also Given that the result is 15 greater than half of that number we get,

• x/2 + 15

According to question,

➞ x/4 + x/3 = x/2 + 15

➞ x/4 + x/3 - x/2 = 15

➞ 3x + 4x - 6x / 12 = 15

➞ x/12 = 15

➞ x = 15 × 12

➞ x = 180

Hence , The number is 180

Verification :

➞ x/4 + x/3 = x/2 + 15

➞ 180/4 + 180/3 = 180/2 + 15

➞ 45 + 60 = 90 + 15

➞ 105 = 105

Hence , Verified

Answer 2

Given :

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• If 1/4 of a number is added to 1/3of the number.
• The result is 15 greater than half of that number.

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To Find : The number.

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☯ Let us considered the number as x.

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• Then as per the condition,

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$\:\::\:\Longrightarrow\:\sf\bigg ({\dfrac{1}{4}}\bigg )x\:+\:\bigg ({\dfrac{1}{3}}\bigg )x\:-\:\bigg ({\dfrac{1}{2}}\bigg )x\:=\:15$

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$\:\:\:\:\::\:\Longrightarrow\:\sf{\dfrac{3x\:+\:4x\:-\:6x}{12}}\:=\:15$

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$\:\:\:\:\:\:\::\:\Longrightarrow\:\sf\bigg ({\dfrac{1}{12}}\bigg )x\:of\:a\:number\:=\:15$

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$\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{x\:=\:15\:\times\:{\dfrac{12}{1}}}$

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$\:\:\:\:\:\:\:\:\:\:\::\:\Longrightarrow\:\sf{x\:=\:180}$

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$\:\:\:\:\therefore\:{\underline{\sf{Hence,\:The\:required\:number\:is\:{\textsf{\textbf{180}}}}}}.$

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$\:\:{\bold{\underline{\sf{\pink{\bold{V\:E\:R\:I\:F\:I\:C\:A\:T\:I\:O\:N\::}}}}}}$

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$\:\:\:\dashrightarrow\:\sf{\dfrac{x}{4}}\:+\:{\dfrac{x}{3}}\:=\:{\dfrac{x}{2}}\:+\:15$

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$\:\:\:\dashrightarrow\:\sf{\dfrac{180}{4}}\:+\:{\dfrac{180}{3}}\:=\:{\dfrac{180}{2}}\:+\:15$

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$\:\:\:\dashrightarrow\:\sf{45\:+\:60\:=\:90\:+\:15}$

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$\:\:\:\dashrightarrow\:\sf{105\:=\:105}$

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$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{\underline{\sf{\textsf{\textbf{Hence\:Verified!!}}}}}$

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