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If 40% of a number is 120, what is 60% of that same number?
150
180
200
240
180
Use the ratio method: Since 40% is 120, then 20% is 60 (by halving both sides). Therefore, 60% is 3 ├Ч20%,which is 3├Ч60=180.
40% of a number is 120.
x=PercentageValueтАЛ├Ч100
Use the ratio method: Since 40% is 120, then 20% is 60 (by halving both sides). Therefore, 60% is 3 ├Ч20%,which is 3├Ч60=180.
Students often calculate the full number (300) first and then find 60% of it, which consumes extra time compared to the direct ratio approach.
Define the relationship
Let the number be x. We are given that 40% of x equals 120. This is represented as:
0.40├Чx=120
Solve for the required percentage
To find 60% of x, we can use the unitary method: 1% of x is 40120тАЛ=3. Therefore, 60% of x is 60├Ч3.
60├Ч3=180
Verification
If the number x=0.4120тАЛ=300, then 60% of 300 is 0.6├Ч300=180.
0.6├Ч300=180
B is correct because calculating the value proportional to the percentage gives the final result of 180.
This concept of proportional scaling is fundamental for solving problems in Profit and Loss, Mixture and Alligation, and Data Interpretation sections.
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