Reverse percentage questions with answers

Questions

1. Question 1A part is known: find the whole

   Vegetables are grown on 25% of a farm. The vegetables cover 300 m². Find the area of the whole farm.

   Show the worked solution

   1. Step 1: Write down what the known percentage stands for$25\% \rightarrow 300$
   2. Step 2: Find 1%$1\% \rightarrow \dfrac{300}{25} = 12$
   3. Step 3: Find 100%$100\% \rightarrow 12 \times 100 = 1200$The farm has an area of $1200$ m².
2. Question 2The value after an increase: find the original

   The monthly rent of a shop went up by 12.5% to $2,700. Find the rent before the increase.

   Show the worked solution

   1. Step 1: Write the new value as a percentage of the original$100\% + 12.5\% = 112.5\%$
   2. Step 2: So this percentage stands for the new value: find 1%$112.5\% \rightarrow 2700$$1\% \rightarrow \dfrac{2700}{112.5} = 24$
   3. Step 3: Find 100%: the original$100\% \rightarrow 24 \times 100 = 2400$The rent before the increase was $2400.
3. Question 3The value after a decrease: find the original

   In a sale, a jacket is sold at 25% off. The sale price is $180. Find the original price.

   Show the worked solution

   1. Step 1: Write the new value as a percentage of the original$100\% - 25\% = 75\%$
   2. Step 2: So this percentage stands for the new value: find 1%$75\% \rightarrow 180$$1\% \rightarrow \dfrac{180}{75} = 2.4$
   3. Step 3: Find 100%: the original$100\% \rightarrow 2.4 \times 100 = 240$The original price was $240.
4. Question 4Find the discount from the sale price

   After a 35% discount, a rice cooker costs $130. Find the amount of the discount.

   Show the worked solution

   1. Step 1: Write the new value as a percentage of the original$100\% - 35\% = 65\%$
   2. Step 2: So this percentage stands for the new value: find 1%$65\% \rightarrow 130$$1\% \rightarrow \dfrac{130}{65} = 2$
   3. Step 3: Find 100%: the original$100\% \rightarrow 2 \times 100 = 200$
   4. Step 4: The discount is the original price minus the sale price$200 - 130 = 70$The discount is $70.
5. Question 5A percentage of the rest: find the total

   Of the people at a concert, 10% are adults. 75% of the rest are teenagers, and the remaining 45 are children. Find the total number of people at the concert.

   Show the worked solution

   1. Step 1: The rest, after the first group: (100% − the first percentage) of the total$100\% - 10\% = 90\%$
   2. Step 2: The last group is (100% − the second percentage) OF THE REST: multiply the two percentages as fractions$\dfrac{25}{100} \times 90\% = 22.5\%$So 22.5\% of the total is $45$.
   3. Step 3: Scale up from the percentage that is known to 100%$\text{Total} = \dfrac{45}{22.5} \times 100$$\phantom{\text{Total}} = 200$There are $200$ people at the concert.