Quantitative Aptitude — MCQ Practice Questions & Answers

Question 1

Two cyclists start simultaneously from the same point and travel in opposite directions on a circular track of 600 m. If their speeds are 8 m/s and 10 m/s respectively, after how much time will they meet again at the starting point?

Accepted Answer

Correct answer: C. 200 seconds — Step 1: Find the time for each cyclist to complete one full lap [Cyclist 1 completes one lap] 	ext{Time}_1 = \frac{	ext{Track length}}{	ext{Speed}_1} = \frac{600}{8} = 75 	ext{ seconds} [Cyclist 2 completes one lap] 	ext{Time}_2 = \frac{	ext{Track length}}{	ext{Speed}_2} = \frac{600}{10} = 60 	ext{ seconds} Step 2: Find the LCM of their lap times [The cyclists will meet at the starting point when the time elapsed is a common multiple of both lap times] 	ext{LCM}(75, 60) = 	ext{LCM of lap times} [Finding prime factorization: 75 = 3 × 5², 60 = 2² × 3 × 5] 	ext{LCM}(75, 60) = 2^2 	imes 3 	imes 5^2 = 4 	imes 3 	imes 25 = 300 	ext{ seconds} Step 3: Verify the answer [In 300 seconds, Cyclist 1 completes] 	ext{Laps}_1 = \frac{300}{75} = 4 	ext{ laps} [In 300 seconds, Cyclist 2 completes] 	ext{Laps}_2 = \frac{300}{60} = 5 	ext{ laps} [Both return to the starting point after completing whole laps

Answer

A. 100 seconds

Answer

B. 150 seconds

Answer

D. 300 seconds

Question 2

A car travels at 60 km/h for the first half of the distance and at 90 km/h for the second half of the distance. What is the average speed for the entire journey?

Accepted Answer

Correct answer: A. 72 km/h — Step 1: Define Variables and Total Distance Let the total distance be D km. The car travels \frac{D}{2} km at each speed. 	ext{Total Distance} = D 	ext{ km} Step 2: Calculate Time for Each Half For the first half at 60 km/h: t_1 = \frac{D/2}{60} = \frac{D}{120} 	ext{ hours} For the second half at 90 km/h: t_2 = \frac{D/2}{90} = \frac{D}{180} 	ext{ hours} Step 3: Calculate Total Time and Average Speed Total time for the journey: t_{	ext{total}} = \frac{D}{120} + \frac{D}{180} = \frac{3D}{360} + \frac{2D}{360} = \frac{5D}{360} = \frac{D}{72} 	ext{ hours} Average speed is total distance divided by total time: 	ext{Average Speed} = \frac{D}{t_{	ext{total}}} = \frac{D}{\frac{D}{72}} = 72 	ext{ km/h} **The average speed for the entire journey is 72 km/h.**

Answer

B. 75 km/h

Answer

C. 70 km/h

Answer

D. 74 km/h

Question 3

A shopkeeper sold two items. Item A was sold at 15% profit and Item B at 10% loss. If the cost price of Item A is ₹4,000 and that of Item B is ₹6,000, and he wants an overall profit of 5%, what should be the selling price of Item B instead?

Accepted Answer

Correct answer: B. 5900 — **To find the required selling price, we need to work backwards from the desired overall profit.** Step 1: **Calculate Selling Price of Item A** Item A is sold at 15% profit on its cost price of ₹4,000. 	ext{Selling Price of A} = 	ext{Cost Price} + 	ext{Profit} = 4000 + (4000 	imes \frac{15}{100}) = 4000 + 600 = ₹4,600 Step 2: **Calculate Total Cost Price and Required Total Selling Price** The total cost price of both items combined is the sum of individual cost prices. 	ext{Total Cost Price} = 4000 + 6000 = ₹10,000 For an overall profit of 5%, the total selling price should be: 	ext{Total Selling Price} = 10000 + (10000 	imes \frac{5}{100}) = 10000 + 500 = ₹10,500 Step 3: **Find Required Selling Price of Item B** Since Total Selling Price = Selling Price of A + Selling Price of B: 	ext{Selling Price of B} = 10500 - 4600 = ₹5,900 **The selling price of Item B should be ₹5,900.** Cost price of Item A =₹4,000 Sold at 15% profit: SP A ​ =4000+15% of 4000 =4000+600=₹4600 Cost price of Item B =₹6,000 Total cost price: 4000+6000=₹10,000 For an overall prof

Answer

A. ₹6,300

Answer

C. ₹6,900

Answer

D. ₹7,200

Question 4

Two sums of money are in the ratio 3:5. They are invested at simple interest rates of 8% and 6% per annum respectively. After 4 years, the difference in their simple interests is ₹480. What are the two principal amounts?

Accepted Answer

Correct answer: C. ₹3,000 and ₹5,000 — Step 1: Set up the principal amounts using the ratio Let the two principal amounts be 3x and 5x respectively, since they are in the ratio 3:5. 	ext{Principal}_1 = 3x, \quad 	ext{Principal}_2 = 5x Step 2: Calculate simple interest for both principals Using the formula SI = (P × R × T)/100, calculate interest for each principal over 4 years. For the first principal at 8% per annum: SI_1 = \frac{3x 	imes 8 	imes 4}{100} = \frac{96x}{100} = 0.96x For the second principal at 6% per annum: SI_2 = \frac{5x 	imes 6 	imes 4}{100} = \frac{120x}{100} = 1.2x Step 3: Find the difference in simple interests and solve for x The difference in simple interests is ₹480. SI_2 - SI_1 = 480 1.2x - 0.96x = 480 0.24x = 480 x = \frac{480}{0.24} = 2000 Step 4: Calculate the two principal amounts Substitute x = 2000 into the principal expressions. 	ext{Principal}_1 = 3x = 3 	imes 2000 = ₹3,000 	ext{Principal}_2 = 5x = 5 	imes 2000 = ₹5,000 **The two principal amounts are ₹3,000

Answer

A. ₹1,500 and ₹2,500

Answer

B. ₹2,400 and ₹4,000

Answer

D. ₹3,600 and ₹6,000

Question 5

A merchant sold two items for ₹2,000 each. On one item he made 25% profit and on the other he made 25% loss. What is his overall profit or loss percentage?

Accepted Answer

Correct answer: B. 6.25% loss — Step 1: Find the Cost Price of the first item (25% profit) If selling price is ₹2,000 with 25% profit, then SP = CP × 1.25 2000 = CP_1 	imes 1.25 CP_1 = \frac{2000}{1.25} = \frac{2000}{\frac{5}{4}} = 2000 	imes \frac{4}{5} = 1600 Step 2: Find the Cost Price of the second item (25% loss) If selling price is ₹2,000 with 25% loss, then SP = CP × 0.75 2000 = CP_2 	imes 0.75 CP_2 = \frac{2000}{0.75} = \frac{2000}{\frac{3}{4}} = 2000 	imes \frac{4}{3} = 2666.67 Step 3: Calculate overall profit or loss percentage Total Cost Price = ₹1,600 + ₹2,666.67 = ₹4,266.67 Total Selling Price = ₹2,000 + ₹2,000 = ₹4,000 	ext{Loss} = CP - SP = 4266.67 - 4000 = 266.67 	ext{Loss\%} = \frac{	ext{Loss}}{	ext{Total CP}} 	imes 100 = \frac{266.67}{4266.67} 	imes 100 = 6.25\% **The merchant made an overall loss of 6.

Answer

A. 6.25% profit

Answer

C. No profit, no loss

Answer

D. 5% loss

Question 6

A wholesaler sells goods to a retailer at 30% discount on marked price. The retailer marks them at 20% above the cost price and gives a discount of 10%. If the marked price is ₹1,000, what is the final selling price?

Accepted Answer

Correct answer: A. ₹756 — Step 1: Marked Price = ₹1000. Wholesaler's SP (Retailer's CP) = 1000 × (1 - 0.30) = ₹700. Step 2: Retailer marks at 20% above CP: New MP = 700 × 1.20 = ₹840. Step 3: Retailer gives 10% discount: Final SP = 840 × 0.90 = ₹756. So option A is correct.

Answer

B. ₹762

Answer

C. ₹770

Answer

D. ₹748

Question 7

Three amounts are invested in the ratio 2:3:5 at simple interest rates of 4%, 5%, and 6% per annum respectively for 2 years. If the total interest earned is ₹1,480, what is the total principal amount invested?

Accepted Answer

Correct answer: C. ₹13,962.26 (approximately)​ — We use the simple interest formula SI = \frac{P 	imes R 	imes T}{100} with amounts in a given ratio to find total principal. **Step 1: Express principals in terms of a variable** Let the three amounts be 2x , 3x , and 5x (in the ratio 2:3:5). The total principal is: P_{total} = 2x + 3x + 5x = 10x **Step 2: Calculate interest for each investment** Using SI = \frac{P 	imes R 	imes T}{100} with T = 2 years: - First amount: SI_1 = \frac{2x 	imes 4 	imes 2}{100} = \frac{16x}{100} = 0.16x - Second amount: SI_2 = \frac{3x 	imes 5 	imes 2}{100} = \frac{30x}{100} = 0.30x - Third amount: SI_3 = \frac{5x 	imes 6 	imes 2}{100} = \frac{60x}{100} = 0.60x **Step 3: Find total interest** SI_{total} = 0.16x + 0.30x + 0.60x = 1.06x **Step 4: Solve for x using given total interest** Given that total interest = ₹1,480: 1.06x = 1480 x = \frac{1480}{1.06} \approx 1396.23 **Step 5: Calculate total principal** P_{total} = 10x = 10 	imes 1396.23 \approx 13,962.26 **Answer: The total principal amount invested is ₹13,962.26 (approximately) (Option C)*

Answer

A. ₹12,000

Answer

B. ₹14,000

Answer

D. ₹15,000

Question 8

A sum of money becomes ₹4,800 in 2 years and ₹5,400 in 3.5 years at simple interest. After how many years from the initial investment will the amount become ₹6,000?

Accepted Answer

Correct answer: B. 5 years — Step 1: SI for (3.5 - 2) = 1.5 years is (5400 - 4800) = ₹600. Step 2: SI for 1 year = 600 / 1.5 = ₹400. Step 3: SI for 2 years = 400 × 2 = ₹800. Principal = 4800 - 800 = ₹4,000. Rate = (400/4000) × 100 = 10% per annum. Step 4: For amount ₹6,000: SI needed = 6000 - 4000 = ₹2,000. Time = (2000 × 100) / (4000 × 10) = 5 years. So option B is correct.

Answer

A. 4.5 years

Answer

C. 4 years

Answer

D. 5.5 years

Quantitative Aptitude - MCQ Practice Questions