# GMAT Ratio Proportion Variation Questions

#### GMAT Sample Questions | Percents & Fractions | Profits | Interest

You could expect around three to six questions that tests concepts in Percentages, Fractions, Decimal fractions, Profit & Loss, Discounts and Simple & Compound interest in the GMAT quant section. Concepts tested include questions equating percentage of a quantity to its value, percentage increase in value, percentage decrease in value, questions with data only in terms of percentage, computing cost price, selling price, percentage profit, percentage discount and profit or loss made, computing simple interest, compound interest, finding amount at the end of a period and computing amount invested at the beginning of a period.

Curated sample GMAT questions from these topics are presented here below. Attempt these questions and check if you have got the correct answer. One can use the explanatory answer or Video explanation made available (wherever provided) to help crack important GMAT quant questions.

1. Three friends Alice, Bond, and Charlie divide $1105 amongs them in such a way that if$10, $20, and$15 are removed from the sums that Alice, Bond, and Charlie received respectively, then the share of the sums that they got will be in the ratio of 11 : 18 : 24. How much did Charlie receive?

1. $495 2.$510
3. $480 4.$375
5. $360 Hint to solve this Ratios word problem Step 1: Assign variables for amounts received by Alice, Bond, and Charlie and frame an equation for total amount received. Step 2: Remove$10, $20, and$15 from amounts received by Alice, Bond, and Charlie respectively and equate it to 11k, 18k, and 24k.
Step 3: Add both the left hand side and right and side of ratio to compute the value of k.
Step 4: Use the value of k to compute 24k and then compute amount received by Charlie.

2. Mary and Mike enter into a partnership by investing $700 and$300 respectively. At the end of one year, they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business. If Mary received $800 more than Mike did, what was the profit made by their business in that year? 1.$2000
2. $6000 3.$4000
4. $1333 5.$3000
Hint to solve GMAT Ratios / Partnership Problem

Step 1: Assume total profit to be 6x. Makes all parts as integers.
Step 2: 4x is divided for investment made and 2x is divided for efforts.
Step 3: 4x is divided in the ratio of their investments. Mary : Mike :: 7 : 3. So, let Mary get 7y and Mike get 3y.
Step 4: Difference in amount got by Mary and Mike = $800. i.e., 7y - 3y = 800. Compute y. Step 5: Use it to compute x. 4x = 10y (step 3). Step 6: Compute 6x to arrive at the answer. 3. A, B, and C each working alone can complete a job in 6, 8, and 12 days respectively. If all three of them work together to complete a job and earn$2340, what will be C's share of the earnings?

1. $1100 2.$520
3. $1080 4.$1170
5. $630 Approach to solve GMAT Work Time Wages Question Concept: Ratio of share of earnings = ratio of work done by A, B, and C. Step 1: Ratio of time taken: A : B : C :: 6 : 8 : 12. Therefore, ratio of work done: $$frac{1}{A} : \frac{1}{B} : \frac{1}{C} = \frac{1}{6} : \frac{1}{8} : \frac{1}{12}$ Step 2: Multiply the work done ratio by the LCM of 6, 8, and 12 to convert the ratio from containing fractions to one that will contain integers. Step 3: Add the resulting values after assigning a factor k and equate it to$2340. Step 4: Compute the value of the factor 'k'. Step 5: Compute C's share. 4. In what ratio should a 20% methyl alcohol solution be mixed with a 50% methyl alcohol solution so that the resultant solution has 40% methyl alcohol in it? 1. 1 : 2 2. 2 : 1 3. 1 : 3 4. 3 : 1 5. 2 : 3 Approach to solve this Mixtures problem Step 1: Let x liters of 20% methyl alcohol be mixed with y liters of 50% methyl alcohol solution. Step 2: What is to be computed? The ratio x : y. Step 3: Methyl alcohol in solution 1 = 20% of x = 0.2x; methyl alcohol in solution 2 = 50% of y = 0.5y. Step 4: Total methyl alcohol = 0.2x + 0.5y...$1)
Step 5: Total volume of mixture = (x + y) liters. Final concentration of methyl alcohol = 40% of (x + y) =0.4(x + y) ... (2)
Step 6: Equate (1) and (2) and compute ratio x : y.

5. If the price of gasoline increases by 25% and Ron intends to spend only 15% more on gasoline, by how much % should he reduce the quantity of gasoline that he buys?

1. 10%
2. 12.5%
3. 8%
4. 12%
5. 6.66%
Hint to solve this GMAT Percents Problem Solving Question

Step 1: Take initial price per unit of gasoline to be $100 and initial volume to be 1 unit. Step 2: Initial amount spent = 100 × 1 =$100
Step 3: Compute new price and new amount spent in reference to the assumed initial price.
Step 4: Equate (new price) × (new volume) = new amount and solve to compute the new volume.
Step 5: Compute change in volume.
Step 6: Compute percentage change in volume to arrive at the answer to this GMAT percentage question.

6. The wages earned by Robin is 30% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin?

1. 23%
2. 18.75%
3. 30%
4. 50%
5. 100%
Approach to solve this Easy Percentages Question

Step 1: Because wages of Robin and Charles are expressed in terms of wages of Erica, assume Erica's wages to be $100. Step 2: Compute wages earned by Robin and Charles. Step 3: Compute how much more Charles earns than Robin. Step 4: Compute by how much % is the wages earned by charles more than that earned by Robin. 7. In an election contested by two parties, Party D secured 12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election? 1. 240,000 2. 300,000 3. 168,000 4. 36,000 5. 24,000 Approach to solve this GMAT Percents Practice Question Step 1: Let Party D get x% of total votes. Step 2: Therefore, Party R would have got (100 - x)% of total votes. Step 3: It is also known that Party R got 12% of total votes lesser than Party D. So, Party R got (x - 12)% of total votes. Step 4: Equate expressions obtained in steps 2 and 3 to compute value of x. Step 5: Equate (x - 12)% of total votes by plugging in value of x and equate it to 132,00 to compute total votes. Step 6: Compute 12% of total votes to find the margin of loss. 8. The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number? 1. 60 2. 80 3. 40 4. 120 5. 160 Hint to solve this Easy GMAT Percents Word Problem Step 1: Let 'x' be the original number. Step 2: Let A be the number obtained when x is increased by 12.5%. Step 3: Let B be the number obtained when x is decreased by 25%. Step 4: Given: (A - B) = 30. Step 5: Substitute A and B in terms of x to compute the value of x. 9. What is the % change in the area of a rectangle when its length increases by 10% and its width decreases by 10%? 1. 0% 2. 20% increase 3. 20% decrease 4. 1% decrease 5. Insufficient data Approach to solve this GMAT Percentages & Areas Question Step 1: Assume values for original length and original width. Let each be 100 units. Step 2: Compute area of rectangle if length = 100 units and width = 100 units. Step 3: Compute new length (10% increase). Compute new width (10% decrease). Compute new area. Step 4: Compute difference in area after change in length and width. Step 5: Compute percentage change in area. 10. If the cost price of 20 articles is equal to the selling price of 25 articles, what is the % profit or % loss made by the merchant? 1. 25% loss 2. 25% profit 3. 20% loss 4. 20% profit 5. 5% profit Approach to solve this Easy GMAT Profits Problem Step 1: Assume the cost price of 1 article to be$1. Compute cost of 20 articles.
Step 2: Equate value of cost of 20 articles to selling price of 25 articles. Compute selling price of 1 article.
Step 3: From information in steps 1 and 2, compute profit of 1 article.
Step 4: Compute % profit or % loss.

11. Sam buys 10 apples for $1. At what price should he sell a dozen apples if he wishes to make a profit of 25%? 1.$0.125
2. $1.25 3.$0.25
4. $1.5 5.$1.8
Hint to solve this Easy Profit Loss Sample Question

Step 1: Compute cost price of a dozen apples.
Step 2: Add 25% profit to cost to arrive at selling price of a dozen apples.

12. By selling an article at 80% of its marked price, a merchant makes a loss of 12%. What % profit will the merchant make if the article is sold at 95% of its marked price?

1. 5% profit
2. 1% loss
3. 10% profit
4. 5.5% profit
5. 4.5% profit
Hint to solve this GMAT Marked Price & Discounts Question

Step 1: Assume cost price of the article to be $100. Let$S be the marked price of the article.
Step 2: 80% of S = 100 - 12% of 100.
Step 3: Solve for S to determine marked price.
Step 4: Compute 95% of S and compare it with cost of $100 and compute profit or loss. Step 5: Compute % profit or % loss. 13. What is the maximum percentage discount that a merchant can offer on her Marked Price so that she ends up selling at no profit or loss, if she had initially marked her goods up by 50%? 1. 50% 2. 20% 3. 25% 4. 16.67% 5. 33.33% Approach to solve this Marked Price Discounts Question Step 1: Assume cost price to be$100.
Step 2: Therefore, marked price = $150. Step 3: Compute discount in dollar terms if she sells at no profit no loss. Step 4: Compute % discount. % discount = $$frac{\text{discount}}{\text{marked price}} \times$ 100 14. A merchant who marked his goods up by 50% subsequently offered a discount of 20% on the marked price. What is the percentage profit that the merchant made after offering the discount? 1. 30% 2. 125% 3. 25% 4. 20% 5. 16.66% Hint to solve this Easy GMAT Profits & Discounts Practice Question Step 1: Assume the cost price to be$100. Step 2: Therefore, marked price = $150. Step 3: Compute dollar value of discount. 20% of marked price. Step 4: Compute final selling price after discount. Step 5: Compute profit or loss made when sold after offering discount. Step 6: Compute % profit or % loss when sold after offering discount. 15. Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 4 times his original investment. What is the value of n? 1. 50 years 2. 25 years 3. 12 years 6 months 4. 37 years 6 months 5. 40 years Hint to solve this GMAT Simple Interest Sample Question Step 1: Assume the initial value of investment to be$100. Step 2: After n years investment becomes $400. Step 3: Therefore, simple interest = 400 - 100 = 300. Step 4: Rate of interest = 8% Step 5: Substitute all values in SI formula. SI = $\frac{\text{principal × number of years × rate of interest}}{100}$ to find the value of number of years. 16. Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received$550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds? 1.$5500 2. $11000 3.$22000 4. $2750 5.$44000 Hint to solve this Simple & Compound Interest Sample Question Step 1: Simple interest for 2 years = $550. Compute simple interest for 1 year. Step 2: Compound interest for 1st year = simple interest for 1st year. Step 3: Compute compound interest for year 1 and year 2. Step 4: Compound interest for year 2 = simple interest on principal + interest on first year's interest Step 5: Compute rate of interest as follows: Rate of interest = $\frac{\text{interest on first year's interest}}{\text{first year's interest}} \times 100$ Step 6: Compute amount invested in simple interest by substituting in SI formula values of SI for 2 years, n = 2 years and rate of interest computedin step 5. Double it to compute total amount invested by Shawn. 17. Ann invested a certain sum of money in a bank that paid simple interest. The amount grew to$240 at the end of 2 years. She waited for another 3 years and got a final amount of $300. What was the principal amount that she invested at the beginning? 1.$200 2. $150 3.$210 4. $175 5. Insufficient data Hint to solve this Easy Simple Interest Practice Question Step 1: Compute interest for 3 years from data about amount at the end of year 2 and the amount at the end of year 5. Step 2: Subtract interest for two years from$240 to compute initial value of investment. 18. Peter invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 3 years and further to$400 at the end of another 5 years. What was the rate of interest in which he invested his sum? 1. 12% 2. 12.5% 3. 6.67% 4. 6.25% 5. 8.33% Hint to solve this Easy Simple Interest Practice Question Step 1: Interest earned for 5 years = 400 - 300 = $100. Step 2: Compute interest for 1 year and interest for 3 years. Step 3: Subtract interest for 3 years from$300 to compute initial value of investment. Step 4: Substitute initial value of investment, interest for 1 year and n = 1 year in simple interest formula to compute rate of interest. 19. Data Sufficiency: If a salesman received a commission of 3% of the sales that he has booked in a month, what was the sales booked by the salesman in the month of November 2003? 1. The sales booked by the salesman in the month of November 2003 minus salesman's commission was $245,000 2. The selling price of the sales booked by the salesman in the month of November 2003 were 125 percent of the original purchase price of$225,000. Approach to solve this GMAT Percents Data Sufficiency Question Question Stem: Commission earned = 3% of sales. Statement 1: Sales booked - 3% sales booked = 245,000. Solving this equation will give a unique value. Statement 1 alone sufficient. Statement 2: Selling price of sales booked = 125% of 225,000. Solving this equation will give a unique answer. Statement 2 alone is also sufficient. 20. John is set to receive two equated annual payments of $x each. He will receive the first of his payments two years from today. Which of the following expressions provides the present value of the two payments if John uses 7% p.a. rate to compute present value? 1. $\frac{\text{$2.07$x}}{$text{$1.07)}^2}) 2. $$frac{\text{$2.07$x}}{$text{$1.07)}^3}) 3. $$frac{$1.07^2 + 1$x}{$text{$1.07)}^3}) 4. $$frac{$2.07^2 + 1$x}{$text{$1.07)}^3}) 5. $$frac{\text{x}}{\text{1.07}}$ + $\frac{\text{x}}{\text{1.07}^2}$ Hint to solve this Compound Interest Practice Question Step 1: Compute present value of first instalment of$x. It will be received 2 years from now at 7% rate of interest. Step 2: Compute present value of second instalment of x. It will be received 3 years from now at 7% rate of interest. Step 3: Sum of values computed in steps 1 and 2 is the answer to the question. #### GMAT Online CourseTry it free! 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