Question Bank - Arithmetic - Shashank Prabhu, CAT 100 Percentiler
Q61) Govind has 2 vessels of equal capacity. The first is filled to capacity with milk and the second if filled to one-third of the capacity with water. The second vessel is now filled to capacity using only the contents of the first vessel. Finally, this process is reversed and the first vessel is filled up to capacity. What is the ratio of milk and water in the first vessel now?
Q63) Hogwarts Express starts from London, King's Cross Station, Platform 9 3/4 and another Hogwarts Express starts from Hogsmeade which is 2160 km far from London. At some point during the journey, the two trains cross each other in 10 seconds. If the length of each of the two trains is 800 m, how much time would it have taken them to meet each other from the time they started their respective journeys?
Q64) 2 men do as much work as is done by 3 children in a day. 5 women do as much work as is done by 3 men in a day. If a man, a woman and a child are employed, it takes 10 days to finish the job. How many days will 2 children working together take to complete the job?
Q71) 10% of a vessel full of milk is drawn off and replaced with water. Then 10% of this mixture is drawn off and replaced with milk. 10% of the mixture is again drawn off and replaced with water. If the vessel now contains 199.1 litres of water, what is the volume of the vessel? (in litres)
Q76) Rani was sneaking candies from the fridge. On the way to her room she encountered her three sisters one after the other one, each of whom had to be given one third of the candies Rani had plus three more to get them promise that they wouldn't tell their mother. In the end, Rani was left with seven candies. How many did she take from the fridge?
Q79) A firm has tractors of four models, A, B, C, D. Four tractors (2 of model B and one each of models C and D) plough a field in two days. Two model A tractors and one model C tractor take three days to do this job. Three tractors one each of models A, B and C take four days to do the same task. How long will it take to do the job if a team is made up of four tractors of different models?
Q90) A milk merchant buys certain number of cans full of milk. If he sells milk at Rs. 13 per litre, he gains Rs. 333. But if he sells milk at Rs. 10 per litre, he loses Rs. 150. How many such cans did be buy, if the capacity of each can is 23 litres?
Q96) A train, 600 m long, starts from Pune to Jammu at 5:40 p.m. At the same time, another train, 350 m long, starts from Jammu to Pune on a parallel track. On the way, the train from Pune crosses a tunnel in 35 seconds while the train from Jammu crosses the same tunnel in 40 seconds. After crossing each other inside the tunnel, the trains reach Jammu and Pune 4 hours and 9 hours later respectively. What is the length of the tunnel?
a. 700 m
b. 450 m
c. 750 m
d. 1050 m
Q99) In a cinema hall. The charge per person is Rs. 200. On the first day, only 60% of the seats were filled. The owner decided to reduce the price by 20% and there was an increase of 50% in the number of spectators on the next day. What was the percentage increase in the revenues on the second day over the first day?
Q1) Instead of dividing Rs. 180 among A, B and C in the ratio (1/3) : (1/4) : (1/6) respectively, it was divided in the ratio 3 : 4 : 6 by mistake. Who gained in this transaction?
Q3) Hiccup was the guest speaker at a seminar on “How to train your dragon” at the Romanian Dragon Sanctuary. He left his office and traveled at a certain speed so that he would reach the Sanctuary on time. After travelling half the distance, he realised that he had left his laptop at his office. He turned back immediately and increased his speed by 50% and reached his office. As compared to his original speed, by what percent should Hiccup increase his speed so that he still reaches the Sanctuary on time?
Q9) There are 4 members in a committee. If one of them is replaced by a younger member such that the average age of the committee is as it was 6 years ago. The new member is how many years younger than the member replaced?
Q10) Two pipes of P and Q can fill a tank A in 10 hrs and 12 hrs respectively. A third pipe R can empty a tank B in 40 hrs. Tank B is two times in volume compared to tank A. If P and Q are kept open to fill tank A and R is connected to empty tank A at the same time such that all the pipes operate simultaneously, how long will take for the tank A to be fully filled?
[OA: 7.5 hours]
Q22) A salesman's commission is 6% on all sales up to Rs. 15000 and 4% on all sales exceeding this amount. He remits Rs. 30000 to his parent company after deducting his commission. Find the total sales.
Q24) At the FMS Alumni meet of 2017, each alumnus brought either 1 or 2 family members. If the ratio of the number of alumni to the number of family members is 3 : 5, what fraction of the alumni brought 2 guests?
Q25) In a cricket match in a parallel universe, Virat and Rohit, each scored 33 before being caught out. This had the effect of lowering Virat's batting average by one run, but raising Rohit's average by one. If, before this match, Virat had scored twice as many runs as Rohit and they had each played the same number of innings, what was Rohit’s new batting average?
Q27) Two planes, which are 2400 km apart, fly toward each other. Their speeds differ by 60 km per hour. They pass each other after 5 hours. Find the speed of the faster plane.
Q39) Three friends are playing a card game. They start with sums of money in the ratio 7 : 6 : 5 and finish with sums of money in the ratio 6 : 5 : 4, in the same order as before. One of them won Rs. 12. How many rupees did he start with? [The three friends gambled amongst each other only]
Q43) Ajay, Vipin and Anil started from the same place and travelled in the same direction at the speeds of 80, 70 and 60 kmph respectively. Vipin started 3 hours after Anil and both Ajay and Vipin overtook Anil at 9.00 p.m. of the same day. Find the time at which Ajay started?
a) 5:15 am
b) 5:30 am
c) 6:00 am
d) 5:45 am
[OA: Option a]
Q44) Jai and Veeru are two masons who are given the job of building a compound wall around a plot owned by Mr. Thakur. Jai working alone takes 8 hours more than the time that both Jai and Veeru would take working together. Veeru working alone takes 12.5 hours more than the time that both would take working together. How many hours would Jai alone take to build the wall?