Question 1

What are the Multiples of 18?

Accepted Answer

The Multiples of 18 are 18, 36, 54, 72, 90, 108, 126, .... Multiples of 18 are nothing but numbers which are divisible by 18 leaving remainder 0. An infinite number of multiples of 18 can be achieved by adding 18 to each subsequent multiple.

Question 2

If you write down all the numbers from 1 to 100, then how many times do you write 3 ?

Accepted Answer

Clearly, From 1 to 100, there are ten numbers with 3 as the unit's digit - 3, 13, 23, 33, 43, 53, 63, 73, 83, 93 and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39. So, required number = 10 + 10 = 20.

Question 3

Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A ?

Accepted Answer

Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A. Then, 2x + 3y = 77 ...(i) and 3x + 2y = 73 ...(ii) Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17. Putting y = 17 in (i), we get: x = 13.

Question 4

A tailor had a number of shirt pieces to cut from a roll of fabric. He cut each roll of equal length into 10 pieces. He cut at the rate of 45 cuts a minute. How many rolls would be cut in 24 minutes ?

Accepted Answer

Number of cuts made to cut a roll into 10 pieces = 9. Therefore, Required number of rolls = (45 x 24)/9 = 120.

Question 5

Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ?

Accepted Answer

Let Varun's age today = x years. Then, Varun's age after 1 year = (x + 1) years. Therefore x + 1 = 2 (x - 12) => x + 1 = 2x - 24 => x = 25.

Question 6

Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married ?

Accepted Answer

Ayush's present age = 10 years. His mother's present age = (10 + 20) years = 30 years. Ayush's father's present age = (30 + 5) years = 35 years. Ayush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years. Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.

Question 7

In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are the…

Accepted Answer

Let R, G and B represent the number of balls in red, green and blue boxes respectively. Then, R + G + B = 108 ...(i), G + R = 2B ...(ii) B = 2R ...(iii) From (ii) and (iii), we have G + R = 2x 2R = 4R or G = 3R. Putting G = 3R and B = 2R in (i), we get: R + 3R + 2R = 108 => 6R = 108 => R = 18. Therefore Number of balls in green box = G = 3R = (3 x 18) = 54.

Question 8

In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If …

Accepted Answer

Let the number of boys and girls participating in sports be 3x and 2x respectively. Then, 3x = 15 or x = 5. So, number of girls participating in sports = 2x = 10. Number of students not participating in sports = 60 - (15 + 10) = 35. Let number of boys not participating in sports be y. Then, number of girls not participating in sports = (35 -y). Therefore (35 - y) = y + 5 <=> 2y<=> 30<=> y = 15. So, number of girls not participating in sports = (35 - 15) = 20. Hence, total number of girls in the class = (10 + 20) = 30.

Question 9

What is the product of all the numbers in the dial of a telephone ?

Accepted Answer

Since one of the numbers on the dial of a telephone is zero, so the product of all the numbers on it is 0.

Question 10

The sum of three consecutive multiples of 3 is 72. What is the second largest number ?

Accepted Answer

Let the numbers be 3x, 3x + 3 and 3x + 6. Then, 3x + (3x + 3) + (3x + 6) = 72 9x = 63 x = 7 Largest number = 3x + 6 = 27. => Second largest number = 27 - 3 = 24

Question 11

A, B, C, D and E play a game of cards. A says to B, "If you give me 3 cards, you will have as many as I have at this moment while if D takes 5 cards from you, he will have as many as E has." A and C together have twice as many cards as E has. B and …

Accepted Answer

Clearly, we have : A = B - 3 ...(i) D + 5 = E ...(ii) A+C = 2E ...(iii) B + D = A+C = 2E ...(iv) A+B + C + D + E=150 ...(v) From (iii), (iv) and (v), we get: 5E = 150 or E = 30. Putting E = 30 in (ii), we get: D = 25. Putting E = 30 and D = 25 in (iv), we get: B = 35. Putting B = 35 in (i), we get: A = 32. Putting A = 32 and E = 30 in (iii), we get: C = 28.

Question 12

Ravi's brother is 3 years senior to him. His father was 28 years of age when his sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, what were the ages of Ravi's father a…

Accepted Answer

When Ravi's brother was born, let Ravi's father's age = x years and mother's age = y years. Then, sister's age = (x - 28) years. So, x - 28 = 4 or x = 32. Ravi's age = (y - 26) years. Age of Ravi's brother = (y - 26 + 3) years = (y - 23) years. Now, when Ravi's brother was born, his age = 0 i.e. y - 23 = 0 or y = 23.

Question 13

7 is to 34 as 5 is to

Accepted Answer

We can get this by any of two explanations. Answer 1: 41 7 = 3 + 4 = 34 Similarly, 5 = 4 + 1 = 41 Answer 2 : 41 7 - 3 = 4 => 34 Similarly, 5 - 4 = 1 => 41

Question 14

A cow was standing on a bridge, 5m away from the middle of the bridge. A train was coming towards the bridge from the ends nearest to the cow. Seeing this cow ran towards the the train and managed to escape when the train was 2m away from bridge. If…

Accepted Answer

let 'b' be the Length of bridge from cow to the near end of the bridge and 'a' be the distance of the train from the bridge. 'x' be speed of cow => '4x' speed of train Then the total length of the bridge 2b + 10. (a-2)/4x = b/x => a-2 = 4b........(1) Now if it had run in opposite direction (a+2b+10-2)/4x = (b+10-2)/x => a - 2b = 24......(2) Solving (1) and (2) b = 11 , Therefore length of the bridge is 2 x 11 + 10 = 32mts.

Question 15

In a certain office, 1/3 of workers are women, 1/2 of the women are married and 1/3 of the married women have children. If 3/4 of the men are married and 2/3 of the married men have children, what part of the workers are without children?

Accepted Answer

Let the total number of workers be x. Then, Number of women = x/3 and number of men = x - x/3 = 2x/3 Number of women having children = x/18 Number of men having children = x/3 Number of workers having children = (x/18) + (x/3) = 7x/18 Therefore, workers having no children = x - 7x/18 = 11/18 of all workers.

Question 16

A man has a certain number of small boxes to pack into parcles. If he packs 3, 4, 5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcle, none is left over. What is the number of boxes, he may have to pack?

Accepted Answer

Clearly, the required number would be such that it leaves a remainder of 1 when divided by 3, 4, 5, or 6 and no remainder when divided by 7. Thus, the number must be of the form (L.C.M of 3, 4, 5, 6) x + 1 i.e., (60x + 1 ) and a multiple of 7. Clearly, for x = 5, the number is a multiple of 7. So the number is 301.

Question 17

The following question is based on the given data for an examination. A. Candidates appeared 10500 B. Passed in all the five subjects 5685 C. Passed in three subjects only 1498 D. Passed in two subjects only 1250 E. Passed in one subject only 835 F.…

Accepted Answer

Candidates passed in atleast four subjects = (Candidates passed in 4 subjects) + (Candidates Passed in all 5 subjects) = (Candidates failed in only 1 subject ) + ( Candidates passed in all subjects) = (78 + 275 + 149 + 147 + 221) + 5685 = 870 + 5685 = 6555

Question 18

Ajay and Vijay have some marbles with them. Ajay told Vijay "if you give me 'x' marbles, both of us will have equal number of marbles". Vijay then told Ajay "if you give me twice as many marbles, I will have 30 more marbles than you would". Find 'x'…

Accepted Answer

If Vijay gives 'x' marbles to Ajay then Vijay and Ajay would have V - x and A + x marbles. V - x = A + x --- (1) If Ajay gives 2x marbles to Vijay then Ajay and Vijay would have A - 2x and V + 2x marbles. V + 2x - (A - 2x) = 30 => V - A + 4x = 30 --- (2) From (1) we have V - A = 2x Substituting V - A = 2x in (2) 6x = 30 => x = 5.

Question 19

In a note collection, there is one new Rs.2000 note for every three old Rs.500 notes. 10 more new Rs.2000 notes are added to the collection and the ratio of new Rs.2000 notes to old Rs.500 notes would be 1: 2. Based on the information, the total num…

Accepted Answer

Let 'x' be the number of new Rs.2000 notes. Given for one new 2000 note there are three old 500 notes. i.e, 3x Given 10 more new Rs.2000 notes are added to the collection and the ratio of new Rs.2000 notes to old Rs.500 notes x + 10 3 x = 1 2 ⇒ x = 20 Therefore, number of new Rs.2000 notes = x+10 = 30. old Rs.500 notes = 3x = 60. Thus, the total number of notes in the collection = 30 + 60 = 90.

Question 20

The cost of 7 tables and 12 chairs is Rs 48,250. What is the cost of 21 tables and 36 chairs ?

Accepted Answer

3T+12C = 48,250----(1) 21T+36C = ? multiply eq (1) with 3 i.e,, 3(7T+12C) = 48,250*3 21T+36C = 1,44,750/-

Arithmetic Reasoning Questions