303 questions asked across 4 exam years, newest first
A metal sphere having a radius of 10 centimetres is melted down and moulded into 8 identical smaller solid spheres. What is the ratio of the surface area of the original sphere to the total surface area of all 8 smaller spheres?
Answer: A
In triangle ABC, medians AD, BE, and CF intersect at the centroid G. What is the ratio of the area of triangle GAB to the area of triangle ABC?
Answer: B
In △ABC, a line segment DE is parallel to BC, with D on AB and E on AC. If the ratio of the area of △ADE to the area of the trapezoid DECB is 4 : 21, what is the ratio of AD to DB?
Answer: A
A ₹36,000 annual bonus is distributed among Sales, Marketing, and Operations in a 4:5:3 ratio. Marketing uses ₹3,000 for team building and ₹1,500 for an intern, then allocates the rest to two top performers in a 5:4 ratio. How much does the top performer with the smaller share receive?
Answer: C
A container holds a mixture of Orange, Apple, and Guava juices in the ratio of 5:7:4 respectively. 24 litres of this mixture is taken out, and then 10 litres of orange juice and 6 litres of guava juice are added to the vessel. If the resultant quantity of apple juice is 14 litres more than the resultant quantity of orange juice, what was the initial quantity of mixture in the vessel (in litres)?
Answer: A
The number of students in two sections A and B having different heights is shown in the table given below: Height (in metres) Section A Section B 1.55 5 4 1.60 9 8 1.62 11 13 1.65 14 10 1.68 6 7 1.71 7 5 1.75 4 3 What is the ratio of the total number of students in Section A whose height is less than 1.65 metres to the total number of students in Section B whose height is less than 1.65 metres?
Answer: B
What should be subtracted from 10, 12, 13, 16 so that the remaining numbers may be proportional?
Answer: C
A drum contains a blend of three chemicals P, Q, and R in the ratio 3 : 5 : 2. 30 litres of this blend are removed, and then 12 litres of chemical P and 8 litres of chemical Q are poured into the drum. If the resultant quantity of chemical Q is 20 litres more than the resultant quantity of chemical P, what was the initial total quantity of the mixture in the drum (in litres)?
Answer: C
A sector of a circle with a radius of 15 cm has a central angle of . Another sector of the same circle has a central angle of radians. What is the ratio of the area of the first sector to the area of the second sector?
Answer: C
The number of red, blue, and green marbles in a bag is in the ratio 3 : 4 : 6. If 20 red marbles, 15 blue marbles, and an unknown number of green marbles are added to the bag, the ratio of red, blue, and green marbles becomes 4 : 5 : 7. Determine the number of green marbles added.
Answer: B
A solution consists of acid and water in the ratio 5 : 3. If 4 litres of water is added, the new ratio becomes 5 : 4. What is the original quantity of acid in the solution?
Answer: A
A tank has a mixture of solutions A, B, and C in the respective ratio of 7 : 8 : 5. 40 litres of this mixture is drained out, and subsequently, 15 litres of solution A and 5 litres of solution C are added to the tank. If the resultant quantity of solution A is 25 litres less than the resultant quantity of solution B, what was the initial quantity of mixture in the tank (in litres)?
Answer: A
The ratio of the time taken by A and B to complete a task is 3 : 2. If B can complete the task alone in 18 hours, how many hours will they take to complete the task if they work together?
Answer: B
In similar triangles, the ratio of corresponding altitudes is 2 : 5. What is the ratio of their areas?
Answer: B
From a 64-liter container of pure spirit, 8 liters are removed and replaced by water. This operation is performed a total of three times. What is the final quantity of spirit remaining in the container?
Answer: D
Determine the ratio of the number of students who play Football to the number of students who play Basketball in a survey of 120 students from the following table: Category Number Play Football and Basketball 25 Play Football but not Basketball 45 Play Basketball but not Football 35 Play neither sport 15
Answer: C
A 75-litre mixture contains milk and water in the ratio 3 : 2. If 15 litres of this mixture are removed and replaced with 10 litres of pure milk, what is the new ratio of milk to water in the mixture?
Answer: B
The ratio of the circumferences of two circular flower beds is 3 : 5. If the smaller flower bed has a radius of 9 m, what is the radius of the larger flower bed?
Answer: A
A rod is divided in the ratio . Total length = 6 m. Find the smallest piece.
Answer: A
Two types of sugar, one costing ₹45/kg and another costing ₹60/kg, are mixed with a third variety in the ratio 1:2:3. If the mixture is worth ₹55/kg, what is the price of the third variety of sugar per kg?
Answer: A
A cone and a hemisphere have the same volume and base radius. Find the ratio of the height of the cone to its radius.
Answer: A
Two circular ponds have circumferences in the ratio 3:5. If the smaller pond has an area of 150 m², what is the approximate area of the larger pond?
Answer: A
A sector has a central angle of and a radius of 8 cm. Another sector of the same circle has a central angle of radians. What is the ratio of the area of the first sector to the area of the second sector?
Answer: A
From a sample of 200 software engineers, determine the ratio of those proficient in Python to those proficient in Java using the given information: Category Number Proficient in Python and Java 50 Proficient in Python only 70 Proficient in Java only 60 Proficient in neither language 20
Answer: B
A 40-liter mixture contains juice and water in the ratio 5:3. How much water (in liters) must be added to this mixture to change the ratio of juice to water to 2:3?
Answer: B
