Arithmetic(Exams > Cat > Quantitaitve Aptitude ) Questions and answers for exam Preparation

Exams > Cat > Quantitaitve Aptitude

ARITHMETIC MCQs

Total Questions : 147 | Page 4 of 15 pages

Question 31. A man travels three-fifth of a distance AB at a speed 3a, and the remaining at a speed 2b. If he goes from B to A and returns at a speed 5c in the same time, then :

1a+1b=1c
a + b = c
1a+1b=2c
None of these

Discuss Question

Answer: Option C. -> 1a+1b=2c
:
C
Approach 1: Conventional Approach :
option (c) time taken to cover AC

= \frac{3 x}{5} \times 3 a = \frac{x}{5 a}

hr.
Time taken to cover CB

= \frac{x}{5 b}

hr.
Time taken to cover BA and back AB

= \frac{2 x}{5 c}

Given

\frac{x}{5 a} + \frac{x}{5 b} = \frac{2 x}{5 c} \to \frac{1}{a} + \frac{1}{b} = \frac{2}{c}

Approach 2:Shortcut using Assumption !
As the questions in terms of variables we can assume values for all the given variables .
Let the distance AB be 5 kms:
The man travels three-fifth of a distance AB at a speed 3a. If we take a=1 we see that he covers a distance of 3 km.The remaining distance of 2 kms is covered in 2b time we get b=1. Also, he goes from B to A and returns at a speed 5c in the same time, we see that c=0.5. Sub these values into the options we find that only (c) fits in. (all the other options get eliminated)

Question 32. A man travels A to B at a speed x km/hr. He then rests at B for x hours. He then travels from B to C at a speed 2x km/hr and rests for 2x hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hr. If distances A-B, B-C and C-D are all equal to 12 km, the time for which he rested at B could be:

3 hr
6hr
2hr
4hr

Discuss Question

Answer: Option A. -> 3 hr
:
A
Using answer options :
Option (a) total time taken from A to D.

\frac{12}{x} + x + \frac{12}{2 x} + 2 x + \frac{12}{4 x} = 16

\to \frac{21}{x} + 3 x = 16

\to 3 x^{2} - 16 x + 21 = 0

\to x = 3, \frac{3}{7}

Alternatively:
Going by the answer options:
Let us assume the answer to be 2 hrs.

\begin{matrix} FROM-TO & Speed & Time taken to cover 12 kms & Rest time & Cumulative time A - B & 2 & 6 & 2 & 8 B - C & 4 & 3 & 4 & 7 C - D & 8 & 1.5 & 0 & 1.5 T o t a l t i m e t a k e n & 16.5 \end{matrix}

Let us assume the answer to be 3 hrs.

\begin{matrix} FROM-TO & Speed & Time taken to cover 12 kms & Rest time & Cumulative time A - B & 3 & 4 & 3 & 7 B - C & 6 & 2 & 6 & 8 C - D & 12 & 1 & 0 & 1 T o t a l t i m e t a k e n & 16 \end{matrix}

Question 33. The petrol consumption rate of a new model car 'Palto' depends on its speed and may be described by the graph below.

Manasa makes a 200 km trip from Mumbai to Pune at a steady speed of 60 km per hour. What is the amount of petrol consumed for the journey?

12.5 litres
13.33 litres
16 litres
19.75 litres

Discuss Question

Answer: Option B. -> 13.33 litres
:
B
Fuel consumption is given in litre per hour. It is, therefore, clear from the graph thatin travelling 60 km fuel consumption is 4 litres. Hence in travelling 200 km fuel consumption will be= 13.33 litres

Question 34. Raman plans to sell his goods at a loss of

8 %

but uses weights of 900 grams in place of a kg weight. Find his real loss or gain percent?

3%
20%
10%
2.22%

Discuss Question

Answer: Option D. -> 2.22%
:
D
Raman plans to sell his goods at a loss of

8 %

. Therefore, Selling Price

= (100 - 8) %

of CP = 0.92 CP. But, when he uses weights that measure only 900 grams while he claims to measure 1 kg.Hence,
CP of 900gms

= 0.90 \times O r i g i n a l C P

So, he is selling goods worth 0.90 CP at 0.92 CP
Therefore, he makes a profit of 0.02 CP on his cost of 0.9 CP profit

% = 2.22 %

Question 35. Of the two machines purchased, the first one’s share of cost is

37.5 %

. Depreciation is to be calculated annually at the rates of

20 %

and

15 %

on the first and second machines respectively, of the value of each machine at the beginning of the year. At the end of two years, the total value of depreciation is what percent of the total cost?

32.94%
33.36%
30.84%
Can’t be determined

Discuss Question

Answer: Option C. -> 30.84%
:
C
Let the cost of two machines be Rs. 800
So, cost of

1^{s t}

machine =

37.5 %

of Rs. 800 = Rs. 300
Cost of

2^{n d}

machine =

62.5 %

of Rs. 800 = Rs. 500
Total cost of 2 machines at the end of 2 yrs = 553.25
Total depreciation

= 246.75 = (\frac{246.75}{800}) \times 100 = 30.84 %

Hence option (c)

Question 36. When price of wheat increased by

44 %

, a family reduced its consumption in such a way that the expenditure on wheat is only

20 %

more than before. If 60 kg of wheat was the previous consumption. The decrease in the consumption is___

Discuss Question

:
Method 1:

Q u a n t i t y \times R a t e = P r i c e

Given : Q1= 60
R1 =r
P1= p
Q2=q
R2=1.44r
P2=1.2p
Hence Q=50
So the difference in price is 50.
Method 2:
Let the price per kg of wheat = Rs 10, hence total expenditure initially = Rs 600
The expenditure increases by

20 %

= Rs 720
Also, the price increases by

44 %

, hence price per kg = 14.4
Thus, new consumption

= \frac{720}{14.4}

= 50 kgs. the diffrence in consumption is 60-50= 10 kg. Option (a)

Question 37. When the air-conditioner is on, a typist can type X pages per hour. However, when the air-conditioner is off, she can type at

65 %

of the earlier efficiency (when the air-conditioner is on). How many hours would she take to type out 575 pages when the air-conditioner is off?

375.4 X
884.6X−1
454.3X−1
None of these

Discuss Question

Answer: Option B. -> 884.6X−1
:
B
Let X=100, Then when AC is off, speed = 65 pages per hour.
Thus to type 575 pages, she takes

\frac{575}{65} = 8.84

pages per hour. Answer is option (b
Alternatively:
When the air-conditioner is off, 0.65X pages are typed per hour. 575 pages will be typed in

\frac{575}{0.65 X} = 884.6 X^{- 1}

Question 38. A particular shop sells goods at cost. A person buys goods worth Rs.60 from the shop and gives the shopkeeper a Rs.100 note. As the shopkeeper does not have change to give his customer, he exchanges this Rs.100 note for 6 Rs.10 notes and 2 Rs. 20 notes from the bank to settle accounts with the customer. The next day, the banker returns the Rs.100 note claiming it to be a counterfeit and takes two Rs.50 notes from the shopkeeper. If the note was actually a counterfeit, what is the total loss to the shopkeeper?

Rs. 200
Rs. 130
Rs. 100
Rs. 60

Discuss Question

Answer: Option C. -> Rs. 100
:
C
The shopkeeper has lost Rs.100 only. The entire transaction can also be viewed as the shopkeeper getting a counterfeit Rs.100 note against which he has given goods worth Rs.60 and change worth Rs.40.

Question 39. When Sunil and Tanuj went for shopping initially Sunil had twice the money than Tanuj. They together bought things amounting to Rs.250. Out of which Tanuj’s share was

60 %

. At the end Sunil was left with thrice the amount that Tanuj had. What was the amount with Tanuj at the beginning___

Discuss Question

:
Initial money with Sunil = s and Tanuj = t
Purchases made by them = Rs. 250
Tanuj’s purchase =

60 %

of Rs. 250 = Rs. 150
Sunil’s purchase = Rs. 250 – Rs. 150 = Rs. 100
So, money left in the end (s – 100) and (t – 150)
Given s = 2t and (s – 100) = 3 (t – 150)
Solving we get t = 350.

Question 40. A