General Awareness:-- Reasoning Part 4
ARITHMETICAL REASONING
ARITHMETICAL REASONING
TYPE
1 : CALCULATION-BASED PROBLEMS
Ex .1. In a chess tournament
each of six players w i l l play every other player exactly once. How
many number of matches will be played in this tournament?
(a) 12 (b) 15 (c) 30 (d) 36
Sol.Clearly, we w i l l
consider the following matches :
(i) matches of first player w
i t h other 5 players;
(ii) matches of second player
w i t h 4 players other t h a n the first player;
(iii) matches of t h i r d
player w i t h 3 players other than the first and second players;
(iv) matches of fourth player
w i t h 2 players other than the first three players; and
(v) match of fifth player w i
t h the sixth one.
So, number of matches played d
u r i n g the tournament = 5 + 4 + 3 + 2 + 1 = 15.
Ex.2. A m a n has a certain
number of small boxes to pack into parcels. If he packs 3, 4, 5 or 6
in a parcel, he is left w i t h one over, if he packs 7 in a parcel,
none is left over. What is the total number of boxes, he may have to pack ?
(a) 106 (b) 301 (c) 309 (d)
400
Sol. Clearly, the required
number would be such t h a t it leaves a remainder of 1 when divided
by 3, 4, 5 or 6 and no remainder when divided by 7. Such a number is
301.
Ex. 3 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 amount of Rs 500 for travelling distance of 80 km how many kms did he travel by taxi ?
(a) 10 (b) 20 (c) 30 (d) 40
Sol. Let assume distance covered
by taxi be x km.
Then, the distance covered by that car
= (80 - x) km.
15x + 5(80 - x) = 500 or 15x +
400 - 5x = 500 or l Q x - 1 0 0 or x= 10.
Distance covered by taxi « 10
km
TYPE
2 : PROBLEMS ON AGES
Ex. 1 Reena is twice as old as
Sunita. Three years ago from now, she was three times as old as Sunita. How
old is Reena now ?
(a) age 6 years (b)age 7 years (c) age 8
years (d) age 12 years
Sol. Let Sunita s present age
be x years.
Then, Reena's present age * 2x
years.
Three years ago, Sunita's age
= (* - 3) and Reena's age = (2x - 3).
So, (2x - 3) - 3(x - 3) or 2x
- 3 - 3x - 9 or x - 6.
Reena s present age = 2x = 12
years.
Hence, the answer is (d).
Ex. 2 The age of a father is twice that of the elder son. Ten years after the age of the father will be three times that of the younger son. If the difference of ages of the two sons of father is 15 years, the age of the father is
(a) 50 years of age (b) 55 years (c)
60 years (d) 70 years
Sol. Let assume that the age of the elder
son be x.
Then, age of younger son = (*
- 15); and
age of the father
= 2x.
So, 2r + 10 = 3(* - 15 + 10)
or 2x+ I0 = 3x - 15 or x = 25.
Father's age * 2 x ~ 5 0
years.
Hence, the answer is (a).
Do it Yourself
1. A shepherd had 17 sheep. A
l l b u t nine died. How many was he left w i t h ?
(a) N i l (b) 8 (c) 9 (d) 17
2. What is the smallest number
of ducks that could swim in this formation — two ducks are in front of a duck, two
ducks behind a duck and a duck is between two ducks ?
(a) 3 (b) 5 (c) 7 (d) 9
3 .A group of 1200 members consisting of captains and soldiers is travelling by a train . For
every 15 soldiers there is one captain. The number of captains in the
group is
(a) 85 (b) 80 (c) 75 (d) 70
4. The number of boy students in a
class is three times the number of girls. Which one of the following
numbers from the list that cannot represent the total number of children in the class ?
(a) 48 (b) 44 (c) 42 (d) 40
5.A motorist knows four
different routes from Bristol to Birmingham . From Birmingham city to Sheffield city he knows three different routes and from Sheffield to
Carlisle he knows two different routes. How many roads he does from Bristol to Carlisle ?
(a) 4 (b) 8 (c) 12 (d) 24
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