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.
Answers
Step-by-step explanation:
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The Number = 40
First Part Of The Number = 15
Second Part Of The Number = 25
Let us assume one part of the number to be 'a'.
If our assumption is correct then according to the question we can assume the other part of the number as 'a + 10'.
The ratio of the numbers that is given to us in the question is = 5:3
Framing A Linear Equation According To The Question:
=> (a + 10)/a = 5/3
Solving The Linear Equation By Cross Multiplication:
=> 3(a + 10) = 5a
=> 3a + 30 = 5a
Taking 3a to the other side of the Equation we get:
=> 30 = 5a - 3a
=> 30 = 2a
Taking 2 to the other side of the Equation we get:
=> a = 30/2
=> a = 15
Therefore, the value we obtained for 'a' is 15.
Therefore, the first part of the number is 15 since we assumed the first part of the number to be'a'.
Calculating the second part of the number as per our assumption:
= a + 10
Putting the value of a:
= 15 + 10
= 25
Therefore, the second part of the number is 25.
Calculating The Number:
= 15 + 25
(As it is divided into two parts)
= 40
Therefore, the number is 40.