Last mile to cat 2012 session2 arithmetic changed

The Last Mile to CAT 2012Session 2

Review of Arithmetic

A, B, C together can complete a piece of work in 6 days. They start together and A leaves after 2 days. B & C finish the remaining work in 7 more days. A alone would have taken how much time to complete the work?

(1) 7 (2) 10 (3) 14 (4) 12

Question 1

Tap A can fill ¾ of a tank & Tap B can fill ¼ of a tank working for a total of 20 minutes between them. Tap B can fill ¾ & tap A ¼ of the same tank in a total of 30 minutes between them. If they work together, how much time would they take to fill the tank?

(a) 10 mins (b) 10.5 min (c) 12 mins (d) data inconsistent

Question 2

If P represents the Principal a represents Equal annual installment and r represents rate of interest per annum and n (no. of years) is 10. Which of the following is necessarily true if the interest is compounded annually?

Question 3

A steamer travels at 5 km/hr in the water. Points A and B are on the same side of a river with B upstream of A. If the distance between A & B is 5 km and the steamer takes 25 min more time to cover distance from A to B as compared to time of travel from B to A, find speed of the stream.

(a) 1 km/hr (b) 2 km/hr (c) 4 km/hr (d) 5 km/hr

Question 4

Arvind got married 24 years ago. At that time his age was his wife’s age plus ½ her age. Presently his age is his wife’s age plus 1/5 her age. What is his age?

(a) 42 (b) 44 (c) 48 (d)52

Question 5

A man buys an article at Rs. 18,000/- in 2007 and sells it at 5% profit. In 2008, the cost price increases by 5% and he increases his selling price by 5%. Because of a market depression in 2009, cost price reduces by 5%. But he increases his selling price by 5%. What is his profit percentage in 2009?

(a) 12% (b) 14 % (c) 15 % (d ) 16 %

Question 6

If a man cycles at 10 km/hr, he arrives at a certain place at 12 noon. If he cycles at 15km/hr, he will arrive at the same place at 10 a.m. At what speed must he cycle to get there at 11 a.m.?

(1)11 km/hr (2) 12 km/hr (3)13 km/hr (4) 14 km/hr

Question 7

Every day 20% of a wall is completed. At the end of the

day, 25% of the wall falls. When will the wall be

completed?

(a) 10 days (b) 8 days (c)12 days (d) None of these

Question 8

Sum of three numbers is 38. The Sum of the first number, 6 times the second number and 4 times the third number is 159. If all the numbers are Prime numbers, what is second number ?

(a) 13  (b) 17  (c) 23  (d) cannot be determined

Question 9

A solution of sugar and water contains 16.67% sugar. 20 kgs of water evaporate. Now the concentration of the solution is 20%. What is the weight of the sugar?

a) 20 b) 120 c) 100 d) 25

Question 10

A and B under take to paint the 4 walls of a square room. The first wall was painted by A alone. He took 5 days more than what would have been taken by both to paint the wall. Then B painted the second wall. He took 45 days more that what would have been taken by both to paint the wall. The third and 4th walls were painted by both together. How will they share the income?

(a) 3:1 (b) 4:1 (c) 5:3 (d) 1:1

Question 11

A man invested Rs. 25,000/- partly at 10% interest and partly at 15%. He received an interest of Rs. 3,250 at the end of the first year if he had invested the amount invested at 10% at 12% what income would he receive on that?

(a) 1200 (b) 1000 (c) 1500 (d) 1400

Question 12

The average speed of a train excluding stoppages is 90kmph. If the stoppages are considered, the average falls down 72 kmph for how many minutes per hour does the train stop?

(a) 10 mins (b) 12 mins (b) 15 mins (b) 18 mins

Question 13

There is a circular track in a park as given in the diagram below. The two circles are concentric. Ashok walks from a point A on the outer wall to the point B on the other side of the outer wall. He walks at a speed of 12kmph. He covers the distance in 50mts. He found the path from A to B was a tangent to the smaller circle. If the radius of the circles are integers, find the difference between the radii of the two circles. (a) 12 (b) 13 (c) 1 (d) 26

00000002

A B

0

C

Question 14

The average age of a family of five members is 5 more than what it would have been today had there been no change in the composition of the family. However, the elder son has since been replaced by a son-in-law. If the age of the elder son 10 years ago was 50, how old is the son-in-law now?

(a) 30 (b) 33 (c) 35 (d) 36

Question 15

Fresh grapes contain 90% water while raisins contain 10% water. If 20 kgs of raisins are made from x kg of fresh grapes, What is the value of x?

a) 160kg b) 180kg c) 200kg d) 190 kg

Question 16

A man wants to reach a certain destination. One-sixth of the

total distance is muddy while half the distance is a tar road. For

the remaining distance he takes a boat. His speeds of

travelling in mud, in water and on the tar road are in the ratio

3:4:5. The ratio of the durations he requires to cross the patch

of mud, stream and tar road is

Question 17

A jewellery shop owner conducts his business in the following manner. Every month he raises his prices by a certain percentage and the next month he reduces his prices by the same percentage. The cycle is repeated once more. After the first such up-down cycle, the price of the jewel decreases by Rs.100. After the second such up-down cycle, the price of the jewel decreases further by Rs.90. What is the initial price of the jewel in Rs.?

a. 1000 b.800 c.900 d.1200

Question 18

The cost prices of two varieties of rice differ by Rs.14. Shyam, the shopkeeper, mixed those two varieties, in certain ratio and resultant mixture costs Rs.20 per kg. If instead, Shyam mixes the two varieties in the inverse ratio, the cost price of the resultant mixture will be Rs.26 per kg. find the cost price (in Rs. per kg) of the less expensive variety of rice. (1) 12 (2) 16 (3) 11 (4) 20

Question 19

Consider the set S = {2, 3, 4, ...., 2n + 1), where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y?(1) 0 (2) 1 (3) n/2 (4) n+1/2n (5) 2008

Question No 20

A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he has sold. What is the current proportion of water to milk?(a) 2:3 (b) 1:2 (c)1:3 (d)3:4

Question No 21

Karan and Arjun run a 100-metre race, where Karan beats Arjun by 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100-metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?(1) Karan and Arjun reach the finishing line simultaneously.(2) Arjun beats Karan by 1 metre.(3) Arjun beats Karan by 11 metres.(4) Karan beats Arjun by 1 metre.

Question No 22

Ram and Shyam run a race between points A and B, 5 km

apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr,

reaches B, and returns to A at the same speed. Shyam

starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches

B and comes back to A at the same speed.

At what time do Ram and Shyam first meet each other?

(1) 10:00 a.m. (2) 10:10 a.m. (3) 10:20 a.m. (4) 10:30 a.m.

Question No 23

Ram and Shyam run a race between points A and B, 5 km apart.

Ram starts at 9 a.m.from A at a speed of 5 km/hr, reaches B,

and returns to A at the same speed. Shyam starts at 9:45 a.m.

from A at a speed of 10 km/hr, reaches B and comes back to A

at the same speed.

At what time does Shyam overtake Ram?

(1) 10:20 a.m. (2) 10:25 a.m. (3) 10:40 a.m. (4) 10:50 a.m.

Question No 24

Arvind exercises for 30 minutes starting at speed and reaches a maximum speed of 10 kmph. The slope is as given in the diagram. What is the average speed?

(30,0)minutes(0,0)

Question No 25