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
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Let one part of the number be x
Then the other part of the number = x + 10
The ratio of the two numbers is 5 : 3
Therefore, (x + 10)/x = 5/3
⇒ 3(x + 10) = 5x
⇒ 3x + 30 = 5x
⇒ 30 = 5x - 3x
⇒ 30 = 2x
⇒ x = 30/2
⇒ x = 15
Therefore, x + 10 = 15 + 10 = 25
Therefore, the number = 25 + 15 = 40
The two parts are 15 and 25
Then the other part of the number = x + 10
The ratio of the two numbers is 5 : 3
Therefore, (x + 10)/x = 5/3
⇒ 3(x + 10) = 5x
⇒ 3x + 30 = 5x
⇒ 30 = 5x - 3x
⇒ 30 = 2x
⇒ x = 30/2
⇒ x = 15
Therefore, x + 10 = 15 + 10 = 25
Therefore, the number = 25 + 15 = 40
The two parts are 15 and 25
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