Arithmetic Problems (CAT PYQs) Part - 1

The speed of a railway engine is 42 kmph when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the train carried by this engine is 24 kmph when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is

Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is ₹700 when there are 25 boarders and ₹600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?

Forty per cent of the employees of a certain company are men, and 75% of the men earn more than ₹25,000 per year. If 45% of the company's employees earn more than ₹25,000 per year, what fraction of the women employed by the company earn less than or equal to ₹25,000 per year?

Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6.30 a.m. and travels at 50 kmph towards Baroda situated 100 km away. At 7.00 a.m. Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 kmph. At 7.30 a.m. Mr Shah, the traffic controller at Baroda realizes that both the trains are running on the same track. How much time does he have to avert a head-on collision between the two trains?

Directions for question: The following table presents the sweetness of different forms relative to sucrose, whose sweetness is taken to be 1.00.

Substance / Sweetness

Lactose 0.16
Maltose 0.32
Glucose 0.74
Sucrose 1.00
Fructose 1.70
Saccharin 675.00

What is the minimum amount of sucrose (to the nearest gram) that must be added to one gram of saccharin to make a mixture that will be at least 100 times as sweet as glucose?

Directions for question: The following table presents the sweetness of different forms relative to sucrose, whose sweetness is taken to be 1.00.

Substance / Sweetness

Lactose 0.16
Maltose 0.32
Glucose 0.74
Sucrose 1.00
Fructose 1.70
Saccharin 675.00

Approximately how many times sweeter than sucrose is a mixture consisting of glucose, sucrose and fructose in the ratio of 1:2:3?

Directions for question: These questions are based on the situation given below. A road network connects cities A, B, C and D. All road segments are straight lines. D is the midpoint on the road connecting A and C. Roads AB and BC are at right angles to each other with BC shorter than AB. The segment AB is 100 km long. Mr. X and Mr. Y leave A at 8:00 am and take different routes to city C, reaching at the same time. X takes the highway from A to B to C and travels at an average speed of 61.875 km per hour. Y takes the direct route AC and travels at 45 km per hour on segment AD. Y's speed on segment DC is 55 km per hour.

What is the average speed of Y in km per hour?

Directions for question: These questions are based on the situation given below. A road network connects cities A, B, C and D. All road segments are straight lines. D is the midpoint on the road connecting A and C. Roads AB and BC are at right angles to each other with BC shorter than AB. The segment AB is 100 km long. Mr. X and Mr. Y leave A at 8:00 am and take different routes to city C, reaching at the same time. X takes the highway from A to B to C and travels at an average speed of 61.875 km per hour. Y takes the direct route AC and travels at 45 km per hour on segment AD. Y's speed on segment DC is 55 km per hour.

The total distance traveled by Y during the journey is approximately

Directions for question: These questions are based on the situation given below. A road network connects cities A, B, C and D. All road segments are straight lines. D is the midpoint on the road connecting A and C. Roads AB and BC are at right angles to each other with BC shorter than AB. The segment AB is 100 km long. Mr. X and Mr. Y leave A at 8:00 am and take different routes to city C, reaching at the same time. X takes the highway from A to B to C and travels at an average speed of 61.875 km per hour. Y takes the direct route AC and travels at 45 km per hour on segment AD. Y's speed on segment DC is 55 km per hour.

What is the length of the road segment BD?

Directions for question: These questions are based on the situation given below.

Rajiv reaches city B from city A in 4 hours, driving at 35 km per hour for the first 2 hours and at 45 km per hour for the next two hours. Aditi follows the same route, but drives at three different speeds: 30, 40 and 50 km per hour, covering an equal distance in each speed segment. The two cars have similar petrol consumption characteristics (km per liter) as shown in the below.

The amount of petrol consumed by Aditi for the journey is