Question Bank - Arithmetic - Shashank Prabhu, CAT 100 Percentiler
Q11) Three Professors Dr. Gupta, Dr. Sharma and Dr. Singh are evaluating answer scripts of a subject. Dr. Gupta is 40% more efficient than Dr. Sharma, who is 20% more efficient than Dr. Singh. Dr. Gupta takes 10 days less than Dr. Sharma to complete the evaluation work. Dr. Gupta starts the evaluation work and works for 10 days and then Dr. Sharma takes over. Dr. Sharma evaluates for next 15 days and then stops. In how many days, Dr. Singh can complete the remaining evaluation work.
[OA: 7.2 days]
Q12) Shyam, Gopal and Madhur are three partners in a business. Their capitals are respectively Rs 4000, Rs 8000 and Rs 6000. Shyam gets 20% of total profit for managing the business. The remaining profit is divided among the three in the ratio of their capitals. At the end of the year, the profit of Shyam is Rs 2200 less than the sum of the profit of Gopal and Madhur. How much profit, Madhur will get?
Q13) A Techno company has 14 machines of equal efficiency in its factory. The annual manufacturing costs are Rs. 42,000 and establishment charges are Rs. 12,000. The annual output of the company is Rs. 70,000. The annual output and manufacturing costs are directly proportional to the no. of machines. The shareholders get 12.5% profit, which is directly proportional to the annual output of the company. If 7.14% machines remain closed throughout the year, then the percentage decrease in the amount of profit of the share holders would be:
d. None of these
Q17) By selling 18 oranges, I lost the selling price of 4 oranges. What is the loss percentage?
d. Can't be determined
Q18) 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
a. 3 : 4 : 2
b. 1 : 1 : 1
c. 6 : 3 : 4
d. 4 : 3 : 6
Q19) Out of the total 390 students studying in a college of Arts and Science, boys and girls are in the ratio of 7 : 6 respectively and the number of students studying Arts and Science are in the ratio of 3 : 7 respectively. The boys and girls studying Arts are in the ratio of 4 : 5 respectively.
How many boys are studying Science?
e) None of these
What is the ratio between the girls studying Arts and Science respectively?
a) 13 : 23
b) 26 : 79
c) 8 : 13
d) 23 : 36
e) None of these
Q21) Salary of an officer increases every year by 20%. His salary in the year 2001 was Rs 26,640. What was his salary in 1999?
(1) Rs 20,000
(2) Rs 19,028
(3) Rs 18,500
(4) Rs 18,840
(5) None of these
Q22) A container contains milk and water in the ratio 3:7 and the other contains 8:11, in what ratio these two containers should be mixed so that the ratio of milk and water is 4:5?
Q25) A, B and C started a business by investing 1/2, 1/3rd and 1/6th of the capital respectively. After 1/3rd of the total time, A withdrew his capital completely and after 1/4th of the total time B withdrew his capital. C kept his capital for the full period. The ratio in which total profit is to be divided amongst the partners is
a. 1 : 2 : 1
b. 4 : 1 : 4
c. 2 : 1 : 2
d. 1 : 2 : 2
Q26) A person buys 18 local tickets for Rs. 110. Each first class ticket costs Rs. 10 and each second class ticket costs Rs. 3. What will another lot of 18 tickets in which the number of first class and second class tickets are interchanged cost?
Q28) The Maximum Retail Price (MRP) of a product is 55% above its manufacturing cost. The product is sold through a retailer, who earns 23% profit on his purchase price. What is the profit percentage (expressed in nearest integer) for the manufacturer who sells his product to the retailer? The retailer gives 10% discount on MRP.
Q29) A milkman mixed 20 L of water with 100 L of milk. He sold one-fifth of the mixture and added as much water to the remaining mixture as the quantity he sold. Find the ratio of water and milk in the mixture now.
Q30) A and B started traveling simultaneously towards each other from two places which are 1260 km apart. They travel with the respective speeds of 130 kmph and 122 kmph. What is the total distance covered by them in the last one minute before they cross each other?
(a) 2.8 km
(b) 3.6 km
(c) 4.2 km
(d) 5.0 km
Q36) A child, playing at the balcony of his multi-storied apartment, drops a ball from a height of 350 m. Each time the ball rebounds, it rises 4/5th of the height it has fallen through. The total distance travelled by the ball before it comes to rest is
Q39) A truck travelling at 70 km/hr uses 30% more diesel to travel a certain distance than it does when it travels at a speed of 50 km/hr. If the truck can travel 19.5 km/L of diesel at 50 km/hr, how far can the truck travel on 10 L of diesel at a speed of 70 km/hr?
Q41) Two farmers were cultivating wheat on their respective agricultural land in a village. Farmer A had an average production of 20 bushels from a hectare. Farmer B, who had 15 hectares of more land dedicated to wheat cultivation, had an output of 30 bushels of wheat from a hectare. If farmer B harvested 530 bushels of wheat more than farmer A, how many bushels of wheat did farmer A cultivate?
Q44) The work done by 4 men in 12 days is equal to the work done by 6 women in 10 days and is also equal to the work done by 8 children in 9 days. A man, a woman, and a child working together take 10 days to complete a particular job, in how many days will the same job be completed by 2 women and 5 children working together?
Q50) In an examination, the average marks obtained by students who passed was x%, while the average of those who failed was y%. The average marks of all students taking the exam was z%. Find in terms of x, y and z, the percentage of students taking the exam who failed.
a. (z - x)/(y - x)
b. (x - z)/(y - z)
c. (y - x)/(z - y)
d. (y - z)/(x - z)
e. (y - z)/(x - y)
Q51) Jugad Singh’s old Bajaj Chetak scooter had a leak in the petrol tank, and was always stuck in the second gear. This meant that he could only travel along at a steady 30 km per hour and managed a paltry 20 km per liter of petrol. Jugad had to start from his village, take CAT 2016 in Patiala and then ride back to his village. At the start of the journey he had exactly 10 liters of fuel in the tank. He knew though, that the fuel tank lost fuel at the rate of half a liter per hour. Just as he arrived home, the scooter stopped because it had run out of fuel. How far is Jugad’s village from his CAT center in Patiala?
Q56) By selling an article at a discount of 25%, a shopkeeper gets Rs. 16 less as profit than by selling it at 50/3% discount. If the cost of 12 articles is equal to the marked price of 8 articles, then find the cost price (in rupees) of each article.