Question

If n is 60% smaller than m, m is what percent greater than n?

Answer 1

To solve this, express n as 40% of m, then calculate the difference between m and n as a percentage of n. The calculation shows that m is 150% greater than n.

Step-by-step explanation:

To determine m as a percent greater than n when n is 60% smaller than m, we can set up an equation. Let m represent the original number, and n will then be 60% less, or 40% of m (since 100% - 60% = 40%). This gives us n = 0.40m. To find how much greater m is than n, we need to compare m - n to n. We have:

m = 1m
n = 0.40m
m - n = 1m - 0.40m = 0.60m

Now, we express this difference as a percentage of n:

0.60m ÷ 0.40m = 1.50

Multiplying by 100 to convert to a percentage, we get:

1.50 × 100% = 150%

Therefore, m is 150% greater than n.

Answer 2

To determine what percent m is greater than n if n is 60% smaller than m, you find that n is 40% of m. Calculating the percentage increase from n to m reveals that m is 150% greater than n.

Step-by-step explanation:

Understanding Percent Decrease and Increase

If n is 60% smaller than m, we can understand this as n being equal to 40% of m, because a 60% decrease implies that what remains is 100% - 60% = 40% of the original. Therefore, n = 0.40m.

To find out what percent m is greater than n, we need to calculate the percentage increase from n to m. If n is 40% of m, to go back to m we need to increase n by 60% of m over the value of n, which is 150% increase.

Here is the step-by-step calculation:

• Let m = 100 (we can use any number to represent m, and 100 makes the math simpler).
• Calculate n which is 60% smaller than m: n = m - 0.60 × m = 100 - 0.60 × 100 = 40.
• To find what percentage m is greater than n, divide the difference by n and multiply by 100: ((m - n) / n) × 100 = ((100 - 40) / 40) × 100 = 150%.

Therefore, m is 150% greater than n.