Arithmetic Practice Questions (Solved) - Shashank Prabhu, CAT 100 Percentiler - Set 2

  • CAT 100%iler, 5 times AIR 1, Director - Learningroots, Ex ITC, Pagalguy, TAS

    Two petrol tanks P1 and P2 contain equal quantities of a mixture of pure petrol and some cheaper fuel. The concentration of petrol is same in both P1 and P2. If 8 litres of mixture in P1 is replaced with pure petrol then the concentration of petrol in P1 becomes twice of what it was initially. If 16 litres of solution from P2 is replaced with pure petrol, then what is the ratio of final concentration of petrol in P2 to the initial concentration of petrol in P2?
    a. 4 : 1
    b. 5 : 2
    c. 3 : 1
    d. 3 : 3

    The concentration of petrol in P1 becomes twice of what it was initially.
    Quantity of petrol initially present in P1 = Net increase of petrol = (8 litres of pure petrol) – (petrol lost in 8 litres of solution in P1)
    Now, 16 litres replacement in P2 can be considered as the replacement of two 8 litres volumes of the solution.
    This will lead to a net increase of two times the initial quantity of petrol. Therefore, this will triple the concentration of petrol in P2. Hence, option c.

    A man is sailing at a uniform speed when a leak develops in his boat. He uses a bucket to empty water from the boat and reaches the shore in 30 minutes just in time to avoid sinking. The leak fills the boat twice as fast as the man is able to empty it. Had the leak developed 10 minutes earlier how much faster would the man have had to work to reach the shore safely?
    a. At least 21% faster
    b. At least 25% faster
    c. At least 37% faster
    d. At least 41% faster

    Let the boat allow 10 liters of water before sinking. If x liters of water are emptied by the person in 30 minutes, 2x liters will enter the boat. So, 2x – x = 10 liters. So, 20 liters enter in 30 minutes and consequently, in 40 minutes, 80/3 liters enter the boat. So, 80/3 – 10 will need to be emptied in 40 minutes. 5/12 liters per minute emptied. Earlier rate of emptying was 1/3 liters per minute. So, he will have to be faster by 25%.

    Three friends Ram, Shyam and Mohan have decided to complete a work together. The time taken by Ram alone to the complete the work is 8(1/3)% more than the time taken by Shyam and Mohan together to complete the work. The time taken by Shyam alone is 25% more than the time taken by Ram and Mohan together to complete the work. If Mohan alone takes 75 days to complete the work, find the time taken by all three of them together to complete the work.
    a. 17/3 days
    b. 16/3 days
    c. 22/3 days
    d. None of these

    R : (S+M) = 12:13, S : (R+M) = 4/5, If there are 225 units, R does 108 units of work, S does 100 units of work, M does 17 units of work. Mohan does 225 units in 75 days. So, he does 17 units in 17/3 days.

    A boy goes from his house to his school daily by a motorbike. He drives the motorbike at three different speeds ‘a’, ‘2.5a’ and ‘4a’ km/hr for three different durations during the journey. He definitely knows the time intervals for which he should drive his motorbike at each of these speeds so as to reach the school on time. On one particular day he starts 20 minutes late from his house and hence the extra time for which he drives his motorbike at ‘2.5a’ km/hr is 6 minutes. Find the extra time for which he drives at ‘4a’ km/hr to reach the school on time.
    a. 11/3 minutes
    b. 15/4 minutes
    c. 13/3 minutes
    d. Cannot be determined

    ax + 2.5ay + 4az = 2.5a(y + 6) + 4a(z + t) + a(x - 20 - 6 - t).
    On solving, you will get t = 11/3 minutes.

    Suresh introduces two schemes for his customers during a festival, on a Fridge whose price is marked at Rs. 15,000. In scheme A he sells the Fridge at a discount of 20 % and in scheme B he sells it at a down payment of Rs. 5000 and 3 installments of Rs. 3,000 each payable at intervals of a year. If he invests his money at simple interest of 10 %, then which offer fetches him a higher sum after three years and how much more is it?
    a. Scheme A, Rs. 1200
    b. Scheme B, Rs. 1200
    c. Scheme B, Rs. 800
    d. Scheme A, Rs. 800

    12000 * 30/100 = 3600 by scheme A.
    5000 * 30/100 + 3000 * 20/100 + 3000 * 10/100 = 2400 by scheme B.
    But he earns Rs. 2000 more on the principal amount as well. Hence, B is better than A by Rs. 800.

    Ramesh and Shyam are competing in 2000 m race. Ramesh gives Shyam a lead of 200 m . Initially Ramesh runs at 4 times Shyam’s speed, but after crossing the 1200 m mark, he slows down to 1/8th of this initial speed, while Shyam continues to run at his original speed. If Ramesh and Shyam meet for the second time at distance ‘a’ m from the finishing line then find ‘a’.

    Let Ramesh be 40 m/s, Shyam be 10 m/s. Ramesh reaches 1200 m after 30 seconds. Shyam covers 300 m in that time. New speed of Ramesh is 5 m/s, distance between Ramesh and Shyam is 700 m. So, they meet after 140 seconds. Shyam covers 1400 m more in this time period. So, total of 1900 m from the start or 100 m from the end.

    A pool is fitted with 3 pipes. The first 2 pipes operating simultaneously fill the pool in the same time during which the pool is filled by the third pipe alone. The second pipe fills the pool 5 hours faster than the first pipe and 4 hours slower than the third pipe. Find the time required by third pipe to fill the pool.
    a. 12 hours
    b. 10 hours
    c. 8 hours
    d. 6 hours

    Let B fill it in x hours.
    (1/x) + (1/(x + 5)) = 1/(x - 4).
    On solving, we get x = 10. So, x - 4 = 6 hours.

    Arun buys a certain number of cards, pads, and DVD’s. 2 DVD’s and 2 pads together can be bought for the cost of 3 cards. If each card had cost Rs. 8 more, then each card would have been worth either 2 DVD’s or 7 pads. The sum of the cost of one pair of each (in units) is

    2d + 2p = 3c
    c + 8 = 2d = 7p
    On substitution, we get c = 6, d = 7, p = 2.
    As one pair of each is asked, it will be 2 * (6 + 7 + 2) = Rs. 30.

    If 2 men can do a work in the same time as can 3 women or 4 children, how many days will it take for 3 men, 4 women and 5 children to do a job which four men take 98 days to complete? If your answer is cannot be determined, mark 0 as your answer.

    2m = 3w = 4c
    4 men do it in 98 days. So, total work is 392m.
    3m + 4w + 5c = 3m + 8m/3 + 5m/2 = 49m/6 per day.
    Number of days = 392*6/49 = 48 days.

    Santosh was the guest speaker at a seminar on “Careers After Class XII” at the Cummins College of Engineering. He left his office and travelled at a certain speed so that he would reach the college on time. After travelling half the distance, he realised that he had left his laptop in 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 Santosh increase his speed so that he still reaches the college on time?

    100 km in 10 hours at 10 km/hr. 50 km in 5 hours covered. 50 km back at 15 km/hr in 10/3 hours. 100 km to be covered in 5/3 hours at 60 km/hr. Increase by 500%

    Anirudh wants to have his bath in a bathtub. There are two taps, one for hot water and one for cold water. Both the taps can individually fill the bathtub in 15 minutes. He opens both the taps simultaneously but after 6 minutes he closes the cold water tap. He lets the hot water tap run until the bathtub fills up. The temperature of the hot water is 50° and of the cold water is 25°. How many degrees is the temperature of the water in the bathtub? Assume that no heat is lost to the surrounding atmosphere.

    Capacity = 15 units. So, 9 units hot water and 6 units cold water. (9 * 50 + 6 * 25)/15 = 40°.

    Cocktail A contains vodka, whisky and rum in the ratio of 1 : 2 : 3 and cocktail B contains the same in the ratio of 3 : 4 : 5. A cocktail C is made by mixing the two cocktails in a certain ratio. Which of the following is an obtainable ratio of vodka, whisky and rum in the new cocktail?
    a) 2 : 5 : 8
    b) 3 : 5 : 7
    c) 5 : 6 : 7
    d) 7 : 9 : 11

    Vodka will be between 2/12 and 3/12 (between 0.167 and 0.25). The only option that satisfies this is option b.

    Mr. Baker runs a bakery shop. One day he made some cakes of different weights. The weight of the heaviest two was 25% of the total weight of all the cakes and the weight of the lightest 5 cakes was 45% the total weight of all cakes. By the end of the day, he was able to sell the 5 lightest cakes. He took the two heaviest cakes home and closed the shop. Next morning he found that all the remaining cakes, which were of same weight, were stolen. How many cakes were stolen?

    100 kg total weight. Heaviest two – 12.5 kg average, lightest 5 – 9 kg average. Remaining cakes – 30 kg total. Also, as the average of the 9 < 30/x < 12.5. So, x = 3.

    The arithmetic mean of a set of 20 observations is X. When three of the twenty observations, 12, 19 and 74 are discarded, the mean of the new set remains unchanged. What is the arithmetic mean, X?

    20X – 105 = 17X
    X = 35.

    An alloy has 35% of A, 40% of B and 25% of C. In each processing step, the percentage of A and B reduces by 20% and 10% respectively and the percentage of C increases. The weight of the alloy does not change. The process stops only when the percentages of A and B become less than 25% and 33.33% respectively. What is the percentage of C at that time?

    A becomes 4/5th of actual and B becomes 9/10th of actual. After the first iteration, it becomes 28, 36, 36. After the second iteration, it becomes 22.4, 32.4, 45.2. So, it will stop after 2 iterations and the percentage of C will be 45.2.

    A car moves with a speed of 90 km/hr with a fuel tank capacity of 100 liters. The mileage of the car is 20 km per litre without switching on the A.C. and 15 km per litre with the A.C. on. The car, with its tank filled to capacity, has to cover a distance of 1600 km without refuelling. What is the distance(in km) that the car can travel with the A.C. switched on?

    a + b = 100
    20a + 15b = 1600; 4a + 3b = 320
    b = 80 liters. So, 15 * 80 = 1200 km.

    A building is to be completed within 40 days. 40 workers started the work, each worker working 8 hours a day. After 25 days, 40% of the work is completed. How many additional workers should be added to the workforce so that the work is completed on time with each worker working for 10 hours a day?

    400 units to be done. In 25 days, 160 units completed. Every day, 160/25 units done by 40 workers over 8 hours. So, 1/50 units per worker per hour. In 10 hours, 1/5 units done by each worker. 240 units to be done in 15 days. So, 16 units per day and so, 80 workers needed in total. So, 40 more workers will be added.

    In a big corporate multinational firm, the employees volunteer to contribute a part of their salary for the prime minister's relief fund for flood victims. The executives each contribute Rs. 4,000 to the fund while the managers contribute twice as much. If the strength of the firm, comprising just of managers and executives, is 1000 and the net collection for the relief fund is Rs. 44,00,000; which of the following statements is true?
    a. The contribution by managers is more than that by the executives by Rs. 28,00,000
    b. The contribution by managers is more than that by the executives by Rs. 44,00,000
    c. The contribution by managers is less than that by the executives by Rs. 28,00,000
    d. The contribution by managers is less than that by the executives by Rs. 16,00,000

    m + e = 1000
    8000m + 4000e = 4400000
    2m + e = 1100
    m = 100, e = 900
    Contribution by managers = 800000, contribution by executives = 3600000.
    Difference is Rs. 28,00,000.

    A and B are athletes. A covers a distance of 1 km in 5 minutes and 50 seconds, while B covers the same distance in 6 minutes and 4 seconds. If both of them start together and run at uniform speed, approximately by what distance will A win a 5 km marathon.
    a. 220 m
    b. 247 m
    c. 192 m
    d. 157 m

    A: 1 km in 350 seconds, 5 km in 1750 seconds
    B: 1 km in 364 seconds, in 1750 seconds, B will cover 4.81 km. So, A wins by approximately 192 m. Option c

    Saatwik drives his car from his house to the station and picks up Seema from there every day at 7.00 p.m. and then they go to the coffeehouse. The coffeehouse is between Saatwik’s house and the station, on the road joining these two places. One day, she reached the station at 6.00 p.m. and instead of waiting for him at the station, she started walking at a speed of 10 km/hr. Saatwik left his house at the usual time and picked her up on his way to the station. If they reached the coffeehouse 20 minutes earlier than usual, what is the speed of Saatwik’s car? (in km/hr)

    10 minutes saved each way. So, Saatwik would have picked her up at 6.50 p.m. So, Seema walks for 50 minutes at 10 km/hr. Saatwik would have covered the same distance in 10 minutes. So, speed of Saatwik is 50 km/hr.

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