Question Bank  Arithmetic  Shashank Prabhu, CAT 100 Percentiler

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?
[OA: C]

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?
[OA: 500%]

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?
[OA: 24]

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.
[OA: 31562.5]

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?
a. 1/2
b. 1/4
c. 1/6
d. 2/3
[OA: 2/3]

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?
[OA: 23]

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.
[OA: 270]

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]
[OA: 420]

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?
[OA: 18]

Q48) The pendulum of a clock takes 7 seconds to strike 4 o'clock. How much time (in seconds) will it take to strike 11 o'clock?
[OA: 70/3]

Q51) Ankhush and Bimal started simultaneously from the same point and drove in opposite directions on a circular track of length 2520 m. initially Ankhush’s speed was 48 m/s and Bimal’s speed was 78 m/s. Each time they met, they interchanged their speeds as well as the direction in which they traveled. Further, it is known that they met for the 46th time at 9:02 pm. When did they meet for the 400th time?
[OA: 11 PM]

Q55) On June 30, 1996, the difference between the ages of Mr. and Mrs. Kapoor was equal to the age of their son Golu. After a few years, when Mr. Kapoor turned 35, Mrs. Kapoor’s age was half the square of Golu’s age then. After another ten years, the difference between the sum of the ages of Mr. and Mrs. Kapoor and that of their son Golu was 69. If Mr. Kapoor is older than his wife, how old will Mrs. Kapoor be on June 30, 2021?
[OA: 52 years]

Q56) Tejas and Swatej were sitting on a bench around the perimeter path of Sarasbaugh, a garden with a circular layout. They saw a dog at the edge of the garden, who was, as the crow flies, 120 meters away from them. Tejas walked towards the dog at 9 km/hr in order to pat it. After patting the dog, he started walking back towards Swatej, who at the same time started walking towards Tejas both taking the shortest route. They met midway on Tejas’ journey back to the bench. In the meantime the dog had taken the radial route to reach the temple, which was at the centre of Sarasbaugh. After meeting, Tejas, Swatej also wanted to have a closer look at the dog. He took the shortest route from their meeting point to reach the temple in 18 seconds. How much had the dog walked to reach the temple?
[OA: 75]

Q58) An athlete, very close to the back end of a train of length 2 km, starts running towards the front end of the train as its front end enters a 4 km tunnel. Both of them are going at a constant speed and the athlete comes out of the tunnel just as train is entirely in the tunnel. When the front end of the train emerges from the tunnel, the athlete turns instantly and heads back towards the front end of the train. How many kilometers from the nearest end of the tunnel does the athlete meet the front end of the train?
a. 1.5
b. 2
c. 2.5
d. 3
[OA: Option a]