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If
40% of a number is 56 and
60% of the same number is 84 , find
100% of that number.
Answer:

If $40 \%$ of a number is $56$ and $60 \%$ of the same number is $84$ , find $100 \%$ of that number. $\newline$ Answer:

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Find the total given a part and a percent

Full solution

Q. If

40 \%

of a number is

56

and

60 \%

of the same number is

84

, find

100 \%

of that number.

\newline

Answer:

Understand Relationship: Understand the relationship between the percentages and the values given. $\newline$ $40\%$ of a number is $56$ . We can express this as an equation: $0.40 \times \text{number} = 56$ .
Calculate Number: Calculate the number based on the $40\%$ value given. $\newline$ To find the number, we divide $56$ by $0.40$ . $\newline$ $\text{number} = \frac{56}{0.40}$ $\newline$ $\text{number} = 140$
Verify Calculation: Verify the calculation with the $60\%$ value given. $\newline$ $60\%$ of the number should be $84$ according to the problem. Let's check if our number is correct. $\newline$ $0.60 \times \text{number} = 0.60 \times 140 = 84$
Confirm Consistency: Confirm that the number found is consistent with both percentage values given. $\newline$ Since both $40\%$ and $60\%$ of the number we found are equal to the values given in the problem ( $56$ and $84$ , respectively), we can conclude that the number is correct.
Find $100$ %: Find $100\%$ of the number. $\newline$ Since we have already found that the number is $140$ when we calculated the $40\%$ value, $100\%$ of the number is simply the number itself. $\newline$ $100\%$ of the number $=$ number $= 140$

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