Question

A number is divided into two parts such that one part is 10 more than the other. If the two
parts are in the ratio 5:3, find the number and the two parts.​

Answer 1

Given :

• Number is divided into 2 parts
• First Number is 10 more than Second Number
• Ratio of two Number = 5:3

Let :

• Number be x
• First part = y
• Second part = z

To find :

• Number (x)
• Two parts (y & z)

Solution :

According to question ,

➝ x = y + z ..... equation 1

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Also , { let y > z }

➝ y = z + 10 .........equation 2

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Ratio of two parts , y : z = 5 : 3

$\sf \implies \: \dfrac{y}{z} = \dfrac{5}{3} \\ \\ \sf \: put \: value \: of \: y \: from \: equation \: 2 \\ \sf \implies \: \dfrac{(z + 10)}{z} \: = \: \dfrac{5}{3} \\ \\ \sf \implies \: 3(z + 10) = 5z \\ \\ \: \sf \implies \: 3z \: + \: 30 \: = \: 5z \\ \\ \sf \implies \: 5z - 3z \: = 30 \\ \\ \sf \implies \: 2z \: = 30 \\ \\ \sf \implies \: z \: = \dfrac{30}{2} \\ \\ \sf \implies \: z \: = 15$

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On Putting (z = 15) in equation 2,

y = 15 + 10

y = 25

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Number (x) = Sum of two parts

x = y + z

x = 25 + 15

x = 40

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ANSWER :

• Number (x) = 40

• Two parts -

1. y = 25
2. z = 15