Question Bank - Arithmetic - Shashank Prabhu, CAT 100 Percentiler
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?
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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?
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?
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 mid-way 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?
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?
[OA: Option a]
Q61) Twelve men are employed to complete a job in 30 days. After 12 days 6 men leave. How many more days over and above the schedule will be required to complete the job if the remaining men increase their working rate by 50%?
Q73) The population of cattle in a farm increases so that the difference between the population in year n + 2 and that in year n is proportional to the population in year n + 1. If the populations in year 2014, 2015 and 2017 were 39, 60 and 123, respectively, then the population in 2016 was
Q82) An instruction was sent to all the railway stations across the country that, workers above the age of 47 years must retire. Five workers with different ages at the Kazipet railway station managed to tamper their records. However, the station master knew that the sums of the ages (in years) of all the possible pairs of workers (from out of the five) are 102, 105, 107, 107, 109, 109, 111, 112, 114, 116. Find the age of the oldest of the five workers.
Q89) Vijay covers 910 km by boat, road and rail in the ratio 4 : 3 : 6 respectively. Surprisingly, the speeds at which the journey was covered were also in the ratio 4 : 3 : 6 respectively. The total time taken for the journey was 89 hours. The ratio of the time taken by boat, road and rail was
[OA: 1 : 1 : 1]
Q90) Four black cows and three brown cows give as much milk in five days as three black cows and five brown cows give in four days. If a black cow gives 10 L of milk per day, then how much milk would be given by a brown cow per day under the same conditions?
Q91) A trader used to make 5% profit on an item selling at usual marked price. One day, he trebled the marked price of the item and finally offered a discount of 30%. Find the percentage profit he made on the item that day.
Q2) For the past k days the average (arithmetic mean) cupcakes per day that Liv baked was 55. Today Bibi joined and together with Liv they baked 100 cupcakes, which raises the average to 60 cupcakes per day. What is the value of k?
Q11) Three friends X, Y and Z have to complete an assignment. Initially, X and Y start working on it. X types at the rate of 4 pages/hr and Y at the rate of 2 pages/hr. When 50 % of the work was done, Z joins in. When the assignment was completed, 80 % of the work was done by X and Z. Find the ratio of work done by X and Z to that by Y when only 80 % of the assignment was completed?
Q14) The average marks scored by two groups X and Y of students are 70 and 75 respectively. Four students are moved from group Y to group X, thereby interchanging the average marks of the two groups. Find the total number of students in two groups put together, if the average marks scored by the four students who moved are 85.
Q17) In a race there were ten athletes running the race and no two of them finished the race in the same position. If there were three girls in the race, what is the probability that the worst position among the girls is five?