IBPS PO Prelims 2025 Quantitative Aptitude Questions with Solutions

Explanation

Compound interest on Rs. 4800 at 10% per annum for 2 years is 4800 × (1.21 - 1) = Rs. 1008. Simple interest on Rs. 5600 at R% for 4 years is (5600 × R × 4) / 100 = 224 R. Given that SI is Rs. 672 more than CI, 224 R - 1008 = 672, which yields 224 R = 1680, so R = 7.5.

Explanation

Profit sharing ratio is based on investment multiplied by time duration. Investment of A is X for 8 months, B is X + 800 for 12 months, and C is 2400 for 4 months. The simplified ratio of investments A : B : C is 2X : 3X + 2400 : 2400. Total relative investment is 5X + 4800. Ratio of B's profit to total profit is (3X + 2400) / (5X + 4800) = 5400 / 9300 = 18 / 31. Solving 31 × (3X + 2400) = 18 × (5X + 4800) gives 3X = 12000, so X = 4000.

Explanation

Since the ratio of boys to girls is 2:1, the weighted average equation is (2 × 22 + 1 × X) / 3 = 20. Simplifying gives 44 + X = 60, which leads directly to X = 16.

Explanation

Let the present ages of A and B be 3x and 2x years respectively. Five years ago, (3x - 5) = 2(2x - 5), which simplifies to x = 5. Thus, the present ages of A and B are 15 years and 10 years. Five years hence, A will be 20 years old and B will be 15 years old, making their total age 35 years. Since C will be 35 years old five years hence, C's present age is 35 - 5 = 30 years.

Explanation

For Set X, the average of seven consecutive even numbers is 630 / 7 = 90, making the numbers 84, 86, 88, 90, 92, 94, and 96. The average of the first four numbers (84, 86, 88, 90) is 87. For Set Y, the average of five consecutive odd numbers is 295 / 5 = 59, making the numbers 55, 57, 59, 61, and 63. The average of the first two numbers (55, 57) is 56, and adding 27 yields 83. Since 87 is greater than 83, Quantity I is greater than Quantity II.

Explanation

The total percentage rate of interest over 5 years is (2 × 10%) + (3 × 15%) = 20% + 45% = 65%. The total simple interest accrued on Rs.6000 is 65% of 6000 = Rs.3900. Since Quantity I equals Rs.3900 and Quantity II is Rs.3900, both quantities are equal.

Explanation

The initial 120 liters mixture contains 45 liters of milk and 75 liters of water. Removing Y liters reduces milk by 3Y/8 and water by 5Y/8. After adding 10 liters of milk and 15 liters of water, the new ratio yields (55 - 3Y/8) / (90 - 5Y/8) = 8 / 13. Solving this equation gives Y = 40. Comparing this to Quantity II (60), Quantity I is less than Quantity II.

Explanation

For Quantity I, the age of the new person is 22 × 64.5 - 21 × 64 = 1419 - 1344 = 75 years. For Quantity II, the sum of ages of 14 family members is 14 × 30 = 420 years. Upon the birth of a baby, the family has 15 members with a total age of 420 years. After 4 years, each member gains 4 years, making the new total age 420 + 15 × 4 = 480 years, and the new average age 480 / 15 = 32 years. Comparing the two values, 75 is greater than 32, so Quantity I is greater than Quantity II.

Explanation

Registered from C = 760. Did not participate from A = 480 - 280 = 200. Ratio = 760:200 = 19:5.

Explanation

Did not participate: C = 760 - 400 = 360, D = 840 - 600 = 240. Average = (360 + 240)/2 = 300.

Explanation

Registered from E = 125% of D = 1.25 x 840 = 1050. Participated from E = 60% of C's participants = 0.60 x 400 = 240. Did not participate from E = 1050 - 240 = 810. Did not participate from D = 840 - 600 = 240. Difference = 810 - 240 = 570.

Explanation

Participated from B = 360. Semifinal qualifiers = 40% of 360 = 144. Final qualifiers = 25% of 144 = 36. Did not qualify for finals = 144 - 36 = 108.

Explanation

Registered from A = 480. Did not participate from C and D together = 360 + 240 = 600. (600 - 480)/600 x 100 = 20% less.

Explanation

Let the interest received from scheme A be P. For scheme B, the compound interest amount is given by P × (1 + 10/100)² = 3630. Simplifying gives P × 1.21 = 3630, so P = 3000. Applying the simple interest formula for scheme A, 3000 = (12500 × r × 2) / 100, which yields 3000 = 250r, giving r = 12.

Explanation

Time taken by Pipe A alone = 6 / 0.25 = 24 hours. Time taken by Pipe B alone = 12 / 0.50 = 24 hours. Pipe C empties in 20 hours. Net rate per hour = 1/24 + 1/24 - 1/20 = 1/12 - 1/20 = 1/30 of the tank. The tank is 60% full, so the remaining portion is 40% = 2/5. Time required = (2/5) / (1/30) = 12 hours.

Explanation

Speed of car A = 480 / 4 = 120 km/h. Speed of car B = 480 / 6 = 80 km/h. Since they move toward each other, their relative speed is 120 + 80 = 200 km/h. Time taken to meet = Total distance / Relative speed = 480 / 200 = 2.4 hours.

Explanation

Since males exceed females by 130 in each company, total females in A = 260 - 130 = 130, and total females in B = 340 - 130 = 210. Non-manager female employees in A = 130 - 60 = 70. Non-manager female employees in B = 210 - 90 = 120. Average number of non-manager female employees = (70 + 120) / 2 = 95.

Explanation

Total male employees in C = 220. Given the ratio of male managers to non-manager males is 7:3, the non-manager male employees in C = 220 × (3 / 10) = 66. Total female employees in company A = 260 - 130 = 130. The difference is 130 - 66 = 64.

Explanation

For each company, female employees equal male employees minus 130. Females in B = 340 - 130 = 210. Total employees in B = 340 + 210 = 550. Females in D = 390 - 130 = 260. Total employees in D = 390 + 260 = 650. Total employees in B and D together = 550 + 650 = 1200. Percentage = (210 / 1200) × 100 = 17.5%.

Explanation

Sum of male and female managers in D = 195 × 2 = 390. Female managers in D = 140, so male managers in D = 390 - 140 = 250. Non-manager male employees in D = 390 - 250 = 140. Sum of female managers in A and B = 60 + 90 = 150. Difference = 150 - 140 = 10.

Explanation

Total employees in B = 340 + 210 = 550. Total employees in E = (3 / 5) × 550 = 330. Male employees in E = 60% of 260 = 156. Female employees in E = 330 - 156 = 174. Female employees in C = 220 - 130 = 90. Female employees in D = 390 - 130 = 260. Total female employees in E, C, and D together = 174 + 90 + 260 = 524.

Explanation

Let Sita's monthly salary be S. Total percentage spent on regular and personal expenses = 30% + 50% = 80%. Remaining salary = 20% of S. Difference between shares of mother and father = (3/4 - 1/4) × 20% of S = 10% of S. Given 10% of S = ₹4,000. S = 4,000 / 0.10 = ₹40,000.

Explanation

Let only art in A = 5x and only art in B = 3x. Both art and music in A = 40% of 5x = 2x. Both art and music in B = 2x + 15. Total art in B = 3x + (2x + 15) = 65, which gives 5x = 50, so x = 10. Thus, only art in A = 50, both in A = 20, and both in B = 35. Total art in A = 50 + 20 = 70. Difference = 70 - 35 = 35.

Explanation

From x = 10, only art in B = 3 × 10 = 30. Total music in A = only music in B + 15 = 45 + 15 = 60. Only music in A = total music in A - both in A = 60 - 20 = 40. Percentage = (40 / 30) × 100 = 133.33%, which rounds to 133.3%.

Explanation

Students who like both art and music in school A = 2 × 10 = 20. Students who like only music in school B = 45. Ratio = 20 : 45 = 4 : 9.

Explanation

Students who like at least two activities refers to those who like both art and music. Students who like both in A = 20. Students who like both in B = 35. Total students in both schools together = 20 + 35 = 55.

Explanation

Students who like at most one activity in school B = (only art in B) + (only music in B) = 30 + 45 = 75. Students who like art in school A = 50 + 20 = 70. Difference = 75 - 70 = 5.

Explanation

Solving equation I gives x = √196 = 14. Solving equation II gives y = ∛2744 = 14. Comparing the values gives x = 14 and y = 14, establishing x = y.

Explanation

For the first equation 18x² + 33x + 14 = 0, splitting the middle term gives (3x + 2)(6x + 7) = 0, yielding x = -2/3 ≈ -0.667 and x = -7/6 ≈ -1.167. For the second equation 8y² + 22y + 15 = 0, splitting the middle term gives (2y + 3)(4y + 5) = 0, yielding y = -3/2 = -1.5 and y = -5/4 = -1.25. Comparing every value of x with every value of y shows that -0.667 and -1.167 are both greater than both -1.5 and -1.25. Therefore, x > y.

Explanation

For 7x² + 27x + 18 = 0, factorizing gives (7x + 6)(x + 3) = 0, so x = -3 and x = -6/7 ≈ -0.857. For 2y² + 13y + 21 = 0, factorizing gives (2y + 7)(y + 3) = 0, so y = -3.5 and y = -3. Comparing the roots, x = -3 is equal to y = -3 and greater than y = -3.5, while x = -0.857 is strictly greater than both values of y. Consequently, x ≥ y.

Explanation

For 2x² + 13x + 21 = 0, factorizing yields (2x + 7)(x + 3) = 0, giving x = -3.5 and x = -3. For y² + 6y + 9 = 0, factorizing yields (y + 3)² = 0, giving y = -3. Comparing x and y values shows -3.5 < -3 and -3 = -3. Thus, x ≤ y.

Explanation

For 3x² - x - 2 = 0, factorizing gives (3x + 2)(x - 1) = 0, so x = 1 and x = -2/3 ≈ -0.667. For 4y² - 2y - 2 = 0, dividing by 2 yields 2y² - y - 1 = 0, which factorizes to (2y + 1)(y - 1) = 0, giving y = 1 and y = -0.5. Comparing x = 1 with y = -0.5 gives x > y, whereas comparing x = -0.667 with y = -0.5 gives x < y. Because contradictory relations exist, no relation can be established between x and y.

Explanation

Approximating the numbers in the equation gives 32% of 750 + ?² = 48% of 1700. Evaluating the percentages: 32% of 750 = 0.32 × 750 = 240, and 48% of 1700 = 0.48 × 1700 = 816. Substituting back into the expression yields 240 + ?² = 816, which simplifies to ?² = 576. Taking the square root gives ? = 24.

Explanation

Rounding the terms to nearest whole integers gives (1152 / ?) + 24% of 450 = 12 × 13. Calculating 24% of 450 gives 0.24 × 450 = 108, and 12 × 13 = 156. Substituting these values gives (1152 / ?) + 108 = 156, leading to 1152 / ? = 48. Solving for ? yields ? = 1152 / 48 = 24.

Explanation

Simplifying the expression using approximate values gives 125% of 420 + 51 = (80% of ?)². Calculating 125% of 420 gives 1.25 × 420 = 525. Adding 51 gives 525 + 51 = 576. Therefore, (0.8 × ?)² = 576. Taking the square root on both sides gives 0.8 × ? = 24. Solving for ? gives ? = 24 / 0.8 = 30.

Explanation

Approximating the terms yields ?³ × 12 + 24% of 450 = 40² + ∛512. Calculating the individual terms gives 24% of 450 = 108, 40² = 1600, and ∛512 = 8. Substituting these into the equation gives 12 × ?³ + 108 = 1600 + 8 = 1608. Subtracting 108 gives 12 × ?³ = 1500, so ?³ = 125. Taking the cube root gives ? = 5.

Explanation

Using nearest integer approximations gives (276 / 12) × (80 / 115) × ? = 32% of 200. Simplifying each fraction, 276 / 12 = 23 and 80 / 115 = 16 / 23. The product becomes 23 × (16 / 23) × ? = 16 × ?. Calculating the right side gives 32% of 200 = 64. Equating both sides gives 16 × ? = 64, which yields ? = 4.

Explanation

Initial mixture contains 150 liters of milk and (y + 30) liters of water, making the total volume (180 + y) liters. Milk fraction in the mixture is 150 / (180 + y). When 35 liters of mixture is removed and replaced with 35 liters of milk, the final milk quantity is given by 150 - 35 × [150 / (180 + y)] + 35 = 160. Simplifying gives 185 - 5250 / (180 + y) = 160, which leads to 5250 / (180 + y) = 25. Thus, 180 + y = 210, giving y = 30 liters.

Explanation

Profit ratio equals the product of investment and time duration. Let Neeraj's investment time be T months, so Vivan's investment time is (T - 2) months. The profit percentage reduction of 28 4/7% equals 2/7, making Neeraj's profit fraction 5/7 of Vivan's profit. Setting up the equation:

(4 × T) / (7 × (T - 2)) = 5 / 7

4T = 5(T - 2) 4T = 5T - 10 T = 10 months

Thus, Vivan invested for 10 - 2 = 8 months.

Explanation

Let the stream speed be u and boat speed in still water be v. Given v : (v + u) = 6 : 7, we get v = 6u, which means downstream speed V_d = 7u and upstream speed Vᵤ = 5u.

Given the time relation: t = 105 / (7u) = 15 / u t + 6 = 90 / (5u) = 18 / u

Subtracting the two time equations: (18 / u) - (15 / u) = 6 3 / u = 6 u = 0.5 km/h

So, V_d = 3.5 km/h and Vᵤ = 2.5 km/h. The total time for a 35 km to-and-fro journey is: Time = (35 / 3.5) + (35 / 2.5) = 10 + 14 = 24 hours.

Explanation

Let the original cost price X = 100k. At a 30% profit, the original selling price Y = 130k. The difference Y - X = 30k.

Under the new conditions: New cost price = 90k New selling price = 130k - 44

Given a 20% profit on the new cost price: 130k - 44 = 1.20 × 90k 130k - 44 = 108k 22k = 44 k = 2

Therefore, Y - X = 30 × 2 = Rs. 60.

Explanation

Speed of train P = 72 × (5/18) = 20 m/s. Speed of train Q = 108 × (5/18) = 30 m/s.

Let the length of train P be L. The platform length is L/2. Train P crosses the platform in 60 seconds: (L + L/2) / 20 = 60 1.5 L = 1200 L = 800 meters

Length of train Q = 2 × 800 = 1600 meters. When running in opposite directions, relative speed = 20 + 30 = 50 m/s. Total distance to cover = 800 + 1600 = 2400 meters. Time to cross = 2400 / 50 = 48 seconds.

Explanation

The perimeter of a rectangle is 2 × (Length + Breadth). 42 = 2 × (Length + 9) Length + 9 = 21 Length = 12 meters

Given that the sum of the length of the rectangle and the side of the square is 36 meters: 12 + Side = 36 Side = 24 meters.