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Two numbers are in ratio 5:7. If their sum is 144, find the smaller number.
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60
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60
Sum the ratio terms (5+7=12) and divide the total (144) by this sum to get the unit value (12). Multiply this unit value by the smaller ratio part (5).
The ratio of two numbers is 5:7 and their sum is 144.
x=Sum┬аof┬аRatio┬аTermsTotal┬аSumтАЛ
Sum the ratio terms (5+7=12) and divide the total (144) by this sum to get the unit value (12). Multiply this unit value by the smaller ratio part (5).
Many students mistake the 'smaller number' for the ratio part itself or calculate the larger number (7├Ч12=84) instead of the smaller one.
Define Ratio Variables
Let the two numbers be 5x and 7x.
5x+7x=144
Solve for x
Add the terms to get 12x=144, then divide by 12 to find the constant x.
x=12144тАЛ=12
Calculate Smaller Number
Multiply the smaller ratio part, which is 5, by the constant x=12.
5├Ч12=60
B is correct because the smaller number is calculated as 60.
This method of finding a 'unit value' is the foundation for solving complex mixtures, partnerships, and age-related problems in competitive exams.
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