Two trains start simultaneously from stations A and B, which are 480 km apart, moving toward each other at 60 km/h and 100 km/h respectively. At the instant the trains start, a bird sitting on the front of the train at A takes off and flies toward the train at B at a constant speed of 200 km/h. As soon as it reaches the other train it instantly turns back, and continues shuttling between the two trains until they meet. What is the total distance (in km) flown by the bird?

A vessel is completely filled with a mixture of milk and water in the ratio 7: 3. From this vessel, 20 litres of the mixture is drawn out and replaced by an equal quantity of water. As a result, the ratio of milk to water in the vessel becomes 21: 29. What is the capacity (in litres) of the vessel?

A trader, while purchasing goods from his supplier, uses a balance whose pan reads “1000 g” when the actual weight placed is 1200g(he gains the extra weight). While selling those same goods to a customer, he uses a different balance whose pan reads “1000 g” when the actual weight given is 800 g. He pays his supplier and charges his customer at the same rate per kg (as displayed by the balance in each case). What is his overall profit percentage?

The average age of a certain group of people is 32 years. When a person aged 60 years joins the group, the average becomes 34 years. Subsequently, two more persons aged x years and 2x years respectively also join the group (in addition to the 60 - year - old), and the average of the resulting group of all members becomes 38 years. What is the value of x?

A shop sold a product in four months. The numbers of units sold in January, February, March and April were 80, 100, 120 and 150, respectively. The cost price was Rs. 320 per unit. A fixed marked price was used in all four months. Discounts of 25%, 15% and 10% were given in January, February and March, respectively, while no discount was given in April. If the total profit over the four months was Rs. 117950, then the marked price per unit, in rupees, was

A car was scheduled to cover a distance of 480 km at a constant speed. After travelling for 2 hours at the scheduled speed, it stopped for 30 minutes. It then increased its speed by 20% and reached the destination 10 minutes before the scheduled arrival time. What was the scheduled speed of the car, in km per hour?

A shopkeeper buys two articles X and Y. He sells X at a profit of 25% on its cost and sells Y at a loss of 20% on its cost. The cost price of Y is 40% more than the cost price of X. If the total selling price of the two articles is Rs. 2370, the cost price of X (in Rs.) is

The average weight of a class of n students is 50 kg. When 10 new students with average weight 60 kg join the class, the average weight of the (now larger) class becomes 52 kg. Some time later, the heaviest 5 students of the new class, with total weight 350 kg, leave the class. The average weight (in kg) of the remaining students is CAT Quant - Hardened Practice Questions

A vessel contains 80 L of pure milk. First, 20% of the contents is drawn out and replaced with water. Then, 25% of the resulting mixture is drawn out and replaced with water. Finally, 50% of the new mixture is drawn out and replaced with water. What is the percentage of milk in the final mixture?

A and B together can complete a job in 12 days, B and C in 15 days, and C and A in 20 days. All three start working together. After 4 days A leaves; 4 days later B also leaves, and C completes the remaining work alone. The total number of days taken to finish the job is:

A store used a fixed marked price for a product and gave a discount of 10% on it. At that selling price, the profit was 20% of the cost price. In the next season, the cost price increased by 25% and the marked price was increased by 20% over the old marked price. The store now wants to earn the same absolute profit per unit as earlier. What discount should be given on the new marked price?

A together in 30 days. A works alone for 8 days. Then B joins A. C joins them only after 70% of the job is completed. From the time C joins, all three together finish the remaining job in 4 days. What is the total number of days taken to complete the job?

A vessel contains 80 litres of pure milk. First, x litres are removed and replaced by water. After thorough mixing, 2x litres of the mixture are removed and replaced by water. If the final ratio of milk to water is 9: 7, what is the value of x, in litres?

A merchant mixes two varieties of grain costing Rs. 70 per kg and Rs. 110 per kg. The total mixture is 120 kg. One - third of the mixture is sold at a profit of 25% on the average cost price per kg of the mixture. One - fourth of the original mixture is lost due to leakage. The remaining quantity is sold at Rs. 136 per kg. If the merchant makes an overall profit of 12.5% on the total cost, what was the ratio of the cheaper grain to the costlier grain in the original mixture?

Three positive numbers a, b, c are in arithmetic progression and

The numbers a, b + 3, and c + 14, in that order, are in geometric progression. What is the value of c -a?