# Ch. 17 :- Arithmetical Reasoning : Exercise 2

23. Jayesh is as much younger to Anil as he is older to Prashant. If the sum of the ages of Anil and Prashant be 48 years, what is the age of Jayesh ?
(a) 20 years
(b) 24 years
(c) 30 years
(d) can not be determined

Ans.(b)
Let the age of Anil and Prashant be x and (48 – x) years, respectively.

Let the age of Jayesh be y years, then
(x – y) = y – (48 – x)
or x – y = y – 48 + x
or 2y = 48,
or y = 24 years

∵ Age of Jayesh is 24 years.

24. Rajan’s age is 3 times than that of Ashok. In 12 years, Rajan’s age will be double the age of Ashok. Rajan’s
present age is

(a) 27 years
(b) 32 years
(c) 36 years
(d) 40 years

Ans.(c)
Let the present age of Ashok be x years
=> the age of Rajan = 3x years.

In 12 years hence, the age of Ashok would be (x + 12) years and that of Rajan be (3x + 12) years.

As given in the question,
(3x + 12) = 2 (x + 12)
or 3x + 12 = 2x + 24
or x = 12 years

Therefore, the age of Rajan = 3 x 12 = 36 years.

25. The age of Arvind’s father is 4 times of his age. If 5 years ago, father’s age was 7 times of the age of his son, what is the age of Arvind’s father at present?
(a) 35 years
(b) 40 years
(c) 70 years
(d) 84 years

Ans.(b)
Let the age of Arvind and his father be x and 4x years, respectively.
Five years ago, the age of Arvind was (x- 5) years and that of his father was (4x – 5) years.

Now, according to the information given in the question,
or (4x – 5) = 7(x – 5)
or 4x – 5 = 7x – 35
3x = 30
or x = 10 years

Therefore, the age of Arvind and his father are 10 years and 40 years, respectively.

26. After five years, the age of a father will be thrice the age of his son, whereas five years ago, he was seven times old as his son was. What is father’s present age?
(a) 35 years
(b) 40 years
(c) 45 years
(d) 50 years

Ans.(b)
Let the age of son after 5 years be x years. Then, the age of father after 5 years would be 3x years.
Five years ago the age of son = (x – 10) years.
Five years ago the age of father = (3x – 10) years

According to the given information in the question,
(3x – 10) = 7 (x – 10)
or 3x – 10 = 7x – 70
or 4x = 60
or x = 15 years

Therefore, present age of father would be (3x – 5) years or (45 – 5) = 40 years.

27. 15 years ago the difference between the ages of two persons was 10 years. The elder one was twice as old as the younger one. The present age of the elder person is
(a) 25 years
(b) 35 years
(c) 45 years
(d) 55 years

Ans.(b)
Let the present age of the elder person be x years.
Then, the present age of the younger person = (x – 10) years.

According to the given information in the question,
(x – 15) = 2 (x – 10 – 15)
or x = 35 years

∵ The present age of the elder person is 35 years.

28. The age of a father 10 years ago was thrice the age of his son. Ten years later, the father’s age will be twice that of his son. The ratio of their present ages is
(a) 8 : 5
(b) 7 : 3
(c) 5 : 2
(d) 9 : 5

Ans.(b)
Let the age of the son 10 years ago be x years.
∵ Father’s age 10 years ago would be 3x years.

Now as per the information given in question,
3x + 20 = 2(x + 20)
or x = 20

∵ Ratio of their present ages
= (3x + 10 : x + 10) = 70 : 30 = 7 : 3

29. Mr. Sohanlal is four times as old as his son. Four years later, the sum of their ages will be 43 years. The present age of the son is
(a) 5 years
(b) 7 years
(c) 8 years
(d) 10 years

Ans.(b)
Let the present age of the son be x years.
Then, the age of Sohanlal would be 4x years.

Four years later, their ages would be (x + 4) and (4x + 4) years, respectively.

Now, as per the information given in the question,
(x + 4) + (4x + 4) = 43
or 5x + 8 = 43
or 5x = 35 years
or x = 7 years

Therefore, the present age of the son is 7 years.

30. A number of friends decided to go on a picnic and planned to spend Rs 96 on eatables. Four of them, however, did not turn up. As a result, the remaining ones had to contribute Rs 4 each extra. The number of those who attended the picnic was
(a) 8
(b) 12
(c) 16
(d) 24

Ans.(a)
Let the number of friends who decided to go on a picnic be x.
Then the contribution of each member = 96x

In case four of them do not turn up, the contribution of each member = 96(x – 4)

Now as per question, 96(x – 4) = 96x + 4
or 1(x – 4)1x496 or x 2 – 4x – 96 = 0
or (x – 12) (x + 8) = 0 or x = 12

Therefore, the number of persons who attended the picnic is (12 – 4) = 8.

31. A, B, C, D and E play game of cards. A says to B, “If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has.” A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have?
(a) 22
(b) 23
(c) 25
(d) 35

Ans.(c)
From the question, we have
B – 3 = E …..(i)
B + 3 = D …..(ii)
A + B = D + E + 10……(iii)
B = C + 2 …….(iv)
A + B + C + D + E = 133 ….(v)

From (i) and (ii),
B – E = D – B => E + D = 2B … (vi)

From (iii) and (vi),
A + B = 2B + 10 => B = A – 10
or A = B + 10 …..(vii)

From (v), (vi), (iv) and (vii), we have
(B + 10) + (B) + (B – 2) + 2B = 133
5B = 133 – 8 = 125
or B = 25

32. A worker may claim Rs 15 for each km which he travels by taxi and Rs 5 for each km which he drives his own car. If in one week he claimed Rs 500 for travelling 80 km, how many km did he travel by taxi?
(a) 10
(b) 20
(c) 30
(d) 40

Ans.(a)
Let the distance covered by taxi be x km.
Then, distance covered by car = (80 – x) km.

15x + 5(80 -x) = 500
or 15x + 400- 5x = 500
or 1Ox = 100
=> x = 10

Therefore, the distance covered by taxi is 10 km.

33. A bus starts from city X. The number of women in the bus is half the number of men. In the city Y, 10 men left the bus and five women boarded in to it. Now, number of men and women becomes equal. In the beginning, how many passengers entered the bus?
(a) 15
(b) 30
(c) 36
(d) 45

Ans.(d)
In the city X let the number of men be x

Then the number of women would be x2
In the city Y, x – 10 = x2 + 5
or x2 = 15 or x = 30 and y = 15

Therefore, total number of passenger in the beginning was 30 + 15 = 45.

34. A, B, C, D and E play 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 Band D together also have the same number of cards as A and C have taken together. If all together they have 150 cards, how many cards has C got?
(a) 28
(b) 29
(c) 31
(d) 35

Ans.(a)
From the question, it is clear that B – 3 = A … (i)
D + 5 = E ……(ii)
A + C = 2E ……(iii)
A + C = B + D ……(iv)
A + B + C + D + E = 150…(v)

From (iii), (iv) and iv), we get
5E = 150
∵ E = 30

Now form (ii), D = 30 – 5 = 25
and form (iv), A = 32
Now form (iii), 32 + C = 2 x 30
C = 60 – 32 = 28

35. Between two book-ends in your study are displayed your five favourite puzzle books. If you decide to arrange the five books in every possible combination and moved just one book every minute, how long would it take?
(a) 1 hrs.
(b) 2 hrs.
(c) 3 hrs.
(d) 4 hrs.

Ans.(b)
No. of ways in which 5 books can be arranged = 5!
= 5 x 4 x 3 x 2 x 1
= 120
So, total time taken= 120 minutes = 2 hours.

36. At the end of a business conference, ten people present shake hands with each other once. How many handshakes will be there all together?
(a) 20
(b) 45
(c) 55
(d) 90

Ans.(b)
Total no. of handshakes = (9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1) = 45

37. I have a few sweets to be distributed. If! keep 2,3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I can have to pack and distribute?
(a) 25
(b) 37
(c) 54
(d) 65

Ans.(a)
The required number will be obtained by taking LCM of 2, 3 and 4 and adding 1 into it. The number so obtained is 25.

38. In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is 9 years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?
(a) 40 years
(b) 50 years
(c) 45 years
(d) 60 years

Ans.(d)
:Let the age of the mother be x years.

∵ Age of the son = x2 years
and the age of daughter = (x2 – 7) years
and the age of the father = 3 ( x2 – 7 ) years
∵ 3(x2 – 7) – X = 9
=> 3x2 – 7 – 21 = 9
=> x2 = 9 + 21 = 30
∵ x = 30 x 2 = 60 years

39. At a farm, there are hens, cows and bullocks and keepers to look after them. There are 69 heads less than legs; the number of cows is double than that of the bullocks; the number of cows and hens is the same and there is one keeper per ten birds and cattle. The total number of hens plus cows and bullocks and their keepers does not exceed 50. How many cows are there?
(a) 10
(b) 14
(c) 12
(d) 16

Ans.(d)
Let the no. of cows be x.
∵ No. of hens = x
and the number of bullocks = x2
∵ No. of keepers = 110( x + x + x2) = x4
∵ Total no. of heads = x + x + x2 + x4 = 11x4
and total no. of legs = 4x + 2x + 2x + 2x4 = 17x2
17x211x4 = 69
23x4 = 69 => x = (69 x 4)23 = 12

40. If the number from 1 to 45 which are exactly divisible by 3 were arranged in ascending order, minimum number being on the top, which would come at the ninth place from the top?
(a) 18
(b) 24
(c) 21
(d) 27

Ans.(d)
3,6,9, … ,45
a = 3,d = 6 – 3 = 3,n = 9
Tn =1 n
T9 = 3 + (9 -1) x 3 = 3 + 24 = 27

41. Out of a total of 120 musicians in a club, 5% can play all the three instruments – guitar, violin and flute. It so happens that the number of musicians who can play any two and only two of the above instruments is 30. The number of musicians who can play the guitar alone is 40. What is the total number of those who can play violin alone or flute alone?
(a) 30
(b) 44
(c) 38
(d) 45

Ans.(b)
5% of 120 = 6
∵ Total number of those who can play violin alone or flute alone
= 120 – (40 + 6 + 30)
= 120 -76
= 44

42. A number of friends decided to go on a picnic and planned to spend Rs 96 on eatables. Four of them did not turn up. As a consequence, the remaining ones had to contribute Rs 4 each extra. The number of those who attended the picnic was
(a) 8
(b) 16
(c) 12
(d) 24

Ans.(a)
Let the number of persons who went for the picnic be x
=> 96x96(x – 4) = 14
96x = 14 + 96(x – 4)
= (4x + 16 + 96)(x – 4)
∵ 96x + 384 = 4x2 + 112 x
∵ 4x2 + 16 x – 384 = 0
∵ x2 + 4 x – 96 = O => (x + 2)(x – 8) = 0
∵ x = 8

43. Ranu is 48 years old. Robin is 6 years junior to Ranu and 14 years senior to Rohit. Ranu has two children – Neethu and Vinu. Youngest sister of Rohit is Krishna and she is 15 years junior to~h What is the age of Krishna?
(a) 13
(b) 15
(c) 14
(d) 12