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The difference between two numbers is 46 and they are in the ratio 5:3. Find the smaller number.
36
63
46
69
69
Calculate the difference in ratio parts (5тИТ3=2). Equate this to the actual difference (2units=46). Find 1unit=23, then multiply by the smaller ratio part (3units=3├Ч23=69).
Difference between two numbers is 46, and the ratio of the numbers is 5 : 3.
x=Ratio┬аDifferenceDifferenceтАЛ
Calculate the difference in ratio parts (5тИТ3=2). Equate this to the actual difference (2units=46). Find 1unit=23, then multiply by the smaller ratio part (3units=3├Ч23=69).
Many students mistake the 'smaller number' for the ratio difference itself or calculate 5units instead of 3units.
Define the numbers in terms of a variable
Since the ratio of the numbers is 5:3, we can represent them as 5x and 3x.
5x,3x
Set up the equation using the given difference
The difference between the two numbers is given as 46.
5xтИТ3x=46
Solve for the common factor x
Simplifying the equation gives 2x=46, which means x=23.
x=246тАЛ=23
Calculate the smaller number
The smaller number is 3x. Substituting x=23, we get 3├Ч23=69.
3├Ч23=69
D is correct because the common ratio factor is 23, and the smaller number 3├Ч23 equals 69.
Always verify your result: 5├Ч23=115 and 3├Ч23=69. 115тИТ69=46, matching the problem statement.
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