IAS Prelims test Math for IAS Prelims Math Challenge

Solution

Correct: C

Let the two numbers be x and y. We are given that x + y = 50 and x - y = 10. Adding these two equations, we get 2x = 60, which implies x = 30. Substituting x = 30 in the first equation, we get 30 + y = 50, which implies y = 20. Therefore, the two numbers are 30 and 20.

Solution

Correct: B

Let the distance between Delhi and Mumbai be x km. The time taken to travel from Delhi to Mumbai is x/60 hours, and the time taken to return is x/40 hours. The total distance traveled is 2x km, and the total time taken is x/60 + x/40 hours. The average speed is given by total distance/total time, which is 2x/(x/60 + x/40) = 2x/(2x/120 + 3x/120) = 2x/(5x/120) = 48 km/h.

Solution

Correct: B

The simple interest is given by the formula I = PRT/100, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time in years. Substituting the given values, we get I = 1000 * 10 * 2 / 100 = 200. Therefore, the total amount after 2 years is 1000 + 200 = 1200.

Solution

Correct: B

The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius. We are given that the area is 16π cm^2. Substituting this value in the formula, we get 16π = πr^2, which implies r^2 = 16. Taking the square root of both sides, we get r = 4 cm.

Solution

Correct: B

The selling price is given by the formula SP = CP + (CP * P/100), where SP is the selling price, CP is the cost price, and P is the profit percentage. Substituting the given values, we get SP = 500 + (500 * 10/100) = 500 + 50 = 550.

Solution

Correct: B

The area of a rectangle is given by the formula A = l * b, where A is the area, l is the length, and b is the breadth. Substituting the given values, we get A = 10 * 5 = 50 cm^2.

Solution

Correct: C

Let the principal amount be P and the rate of interest be R. We are given that the amount becomes triple in 10 years, which means the amount after 10 years is 3P. The simple interest is given by the formula I = PRT/100, where I is the interest. Since the amount after 10 years is 3P, the interest is 2P. Substituting these values in the formula, we get 2P = P * R * 10 / 100, which implies R = 20.

Solution

Correct: D

The surface area of a cube is given by the formula SA = 6s^2, where SA is the surface area and s is the side length. Substituting the given value, we get SA = 6 * 6^2 = 6 * 36 = 216 cm^2.

Solution

Correct: A

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. We are given that the circumference is 22 cm. Substituting this value in the formula, we get 22 = 2 * (22/7) * r, which implies r = 22 * 7 / 44 = 3.5 cm.

Solution

Correct: C

The loss is given by the formula L = CP - SP, where L is the loss, CP is the cost price, and SP is the selling price. We are given that the cost price is Rs. 100 and the selling price is Rs. 80. Substituting these values, we get L = 100 - 80 = 20. The loss percentage is given by the formula LP = (L/CP) * 100, where LP is the loss percentage. Substituting the values, we get LP = (20/100) * 100 = 20.

Solution

Correct: B

The average speed is given by the formula AS = Total Distance / Total Time, where AS is the average speed. We are given that the total distance is 250 km and the total time is 5 hours. Substituting these values, we get AS = 250 / 5 = 50 km/h.

Solution

Correct: B

The amount after 2 years is given by the formula A = P(1 + R/100)^T, where A is the amount, P is the principal amount, R is the rate of interest, and T is the time in years. Substituting the given values, we get A = 1000(1 + 10/100)^2 = 1000 * (1.1)^2 = 1000 * 1.21 = 1210.

Solution

Correct: C

The area of a triangle is given by the formula A = (1/2) * b * h, where A is the area, b is the base, and h is the height. We are given that the area is 60 cm^2 and the base is 10 cm. Substituting these values in the formula, we get 60 = (1/2) * 10 * h, which implies h = 60 * 2 / 10 = 12 cm.

Solution

Correct: B

Let the principal amount be P and the rate of interest be R. We are given that the amount becomes double in 5 years, which means the amount after 5 years is 2P. The compound interest is given by the formula A = P(1 + R/100)^T, where A is the amount, P is the principal amount, R is the rate of interest, and T is the time in years. Substituting the values, we get 2P = P(1 + R/100)^5, which implies (1 + R/100)^5 = 2. Taking the fifth root of both sides, we get 1 + R/100 = 2^(1/5), which implies R = (2^(1/5) - 1) * 100 ≈ 14.87. However, the closest option to this is 15%.

Solution

Correct: B

The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height. Substituting the given values, we get V = (22/7) * 7^2 * 10 = (22/7) * 49 * 10 = 1540 cm^3. However, the closest option to this is 1500 cm^3.

Solution

Correct: A

The total distance traveled is 60 + 40 = 100 km, and the total time taken is 2 + 1 = 3 hours. The average speed is given by the formula AS = Total Distance / Total Time, where AS is the average speed. Substituting the values, we get AS = 100 / 3 ≈ 33.33 km/h. However, the closest option to this is 30 km/h.

Solution

Correct: C

The volume of a cube is given by the formula V = s^3, where V is the volume and s is the side length. We are given that the volume is 1000 cm^3. Substituting this value in the formula, we get 1000 = s^3, which implies s = ∛1000 = 10 cm.

Solution

Correct: B

The cost price of 100 articles is 100 * 50 = Rs. 5000. The selling price of each article is 50 + (50 * 10/100) = 55. The total selling price of 100 articles is 100 * 55 = Rs. 5500. The total profit is given by the formula TP = Total Selling Price - Total Cost Price, where TP is the total profit. Substituting the values, we get TP = 5500 - 5000 = 500.

Solution

Correct: D

Let the principal amount be P and the rate of interest be R. We are given that the amount becomes four times in 8 years, which means the amount after 8 years is 4P. The simple interest is given by the formula I = PRT/100, where I is the interest. Since the amount after 8 years is 4P, the interest is 3P. Substituting these values in the formula, we get 3P = P * R * 8 / 100, which implies R = (3 * 100) / 8 = 37.5.

Solution

Correct: B

The perimeter of a rectangle is given by the formula P = 2(l + b), where P is the perimeter, l is the length, and b is the breadth. Substituting the given values, we get P = 2(15 + 8) = 2 * 23 = 46 cm.

Solution

Correct: B

The amount after 3 years is given by the formula A = P(1 + R/100)^T, where A is the amount, P is the principal amount, R is the rate of interest, and T is the time in years. Substituting the given values, we get A = 5000(1 + 12/100)^3 = 5000 * (1.12)^3 = 5000 * 1.404928 = 7024.64. However, the closest option to this is Rs. 7000.

Solution

Correct: B

The radius of the cylinder is given by the formula r = d/2, where r is the radius and d is the diameter. Substituting the given value, we get r = 14/2 = 7 cm. The volume of the cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height. Substituting the values, we get V = (22/7) * 7^2 * 10 = (22/7) * 49 * 10 = 1540 cm^3. However, the closest option to this is 1500 cm^3.