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Two numbers are in the ratio 4:7. If the larger number is decreased by 10 and the smaller number is increased by 10, the numbers become equal. What is the original larger number?
Question ID : 4410092017266 Option 1 ID : 4410097943178 Option 2 ID : 4410097943175 Option 3 ID : 4410097943176 Option 4 ID : 4410097943177 Status : Answered Chosen Option : D
Question ID : 4410092017266 Option 1 ID : 4410097943178 Option 2 ID : 4410097943175 Option 3 ID : 4410097943176 Option 4 ID : 4410097943177 Status : Answered Chosen Option : D
Calculate the difference between the ratio parts (7тИТ4=3 units). This difference corresponds to 10+10=20 difference in absolute values. Thus, 3┬аunits=20. However, since they become equal, 4x+10=7xтИТ10, so 3x=20, x=20/3. The larger number is 7x=7├Ч(20/3)=140/3=46.67.
Two numbers are in the ratio 4:7. The larger number is decreased by 10 and the smaller number is increased by 10, resulting in the numbers becoming equal.
7xтИТ104x+10тАЛ=1
Calculate the difference between the ratio parts (7тИТ4=3 units). This difference corresponds to 10+10=20 difference in absolute values. Thus, 3┬аunits=20. However, since they become equal, 4x+10=7xтИТ10, so 3x=20, x=20/3. The larger number is 7x=7├Ч(20/3)=140/3=46.67.
Students often misinterpret 'decreased by 10' as subtracting from the variable instead of the value or confuse the order of the numbers in the ratio.
Define variables
Let the two numbers be 4x and 7x.
Numbers=4x,7x
Set up the equation
According to the problem, decreasing the larger number (7x) by 10 and increasing the smaller number (4x) by 10 makes them equal.
4x+10=7xтИТ10
Solve for x
Rearrange the equation to solve for x: 10+10=7xтИТ4x, which simplifies to 20=3x.
x=320тАЛ
Calculate the larger number
The larger number was defined as 7x. Substituting the value of x gives 7├Ч(20/3)=140/3.
Larger┬аNumber=7├Ч320тАЛ=3140тАЛ=46.66...
D is correct because based on the linear equation 4x+10=7xтИТ10, we find x=20/3, making the larger number 7├Ч(20/3)=46.67.
This concept of equalizing values after change is frequently used in 'Age Problem' questions where adding/subtracting years changes the ratio of ages.
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