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Two numbers are in the ratio 4:1. If difference between the numbers is 54, then find the greater number.
72
42
90
56
72
Since the ratio is 4:1, the difference is 3 parts (4-1=3). Given 3 parts = 54, 1 part = 18. Greater number is 4 parts, so 4 ├Ч 18 = 72.
Two numbers are in the ratio 4 : 1. The difference between the numbers is 54.
n1тАЛ=4x,n2тАЛ=x,n1тАЛтИТn2тАЛ=54
Since the ratio is 4:1, the difference is 3 parts (4-1=3). Given 3 parts = 54, 1 part = 18. Greater number is 4 parts, so 4 ├Ч 18 = 72.
Students often forget to find the greater number and accidentally provide the value of the smaller number (18) or the common ratio factor (18) as the final answer.
Define the numbers in terms of a variable
Since the numbers are in the ratio 4: 1, we can represent the numbers as 4x and x.
n1тАЛ=4x,n2тАЛ=x
Set up the equation based on the difference
The difference between the two numbers is given as 54, so we subtract the smaller number from the greater one: 4xтИТx=54.
3x=54
Solve for x
Divide 54 by 3 to find the value of one part.
x=354тАЛ=18
Calculate the greater number
The greater number is 4x. Substituting x=18, we get 4├Ч18=72.
GreaterNumber=4├Ч18=72
A is correct because the greater number is 4 times the unit value of 18, which equals 72.
This concept is a foundation for mixture and allegation problems; always represent ratio units as variables to simplify multi-step calculations.
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