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

Exams > Cat > Quantitaitve Aptitude

ARITHMETIC MCQs

Total Questions : 147 | Page 5 of 15 pages

Question 41. There is an alloy (A) of silver and copper. A certain weight of this alloy is mixed with 15 kg of pure Silver and melted. The new alloy (B) contains

90 %

of silver. If the alloy (A) is mixed with 10kg of a

90 %

silver alloy, the new alloy (C) is found to contain

84 %

silver. Find the percentage of silver in (A).

Discuss Question

Answer: Option A. -> 80%
:
A
Use alligation and then the answer options
Let the percentage of silver in alloy A be a

There Is An Alloy (A) Of Silver And Copper. A Certain Weight...

Now substitute values from answer options such that all the criteria are satisfied. Answer is option (a) as shown below

Question 42. Sajan lent Rs. 7000 to two of his friends: to one at

4 %

and to other at

6 %

SI. The total amount received as interest by Sajan after 3 years is Rs. 996. Find the amount lent at

6 %

Rs. 1300
Rs. 2600
Rs. 4400
Rs. 1600

Discuss Question

Answer: Option B. -> Rs. 2600
:
B
Principal = Rs. 7000
Interest Received = Rs. 996
So, average rate

= \frac{(996 \times 100)}{3 \times 7000} = \frac{166}{35} %

Now apply alligation:

Sajan Lent Rs. 7000 To Two Of His Friends: To One At 4% And ...

So, the ratio in which the money was lent at

4 %

and

6 %

is 22: 13
So, the amount lent at

6 %

= Rs. 2600. Hence option (b)
Alternatively: the question can be solved using answer options.

Question 43. In a company, there are initially ‘n’ employees. First

p %

employees were hired and after a month

q %

of the employees were fired. This again made the number of employees in the company as ‘n’. Find the value of p – q.

pq100
pq
p+q100
2np

Discuss Question

Answer: Option A. -> pq100
:
A

n (1 + \frac{p}{100}) (1 - \frac{q}{100}) = n / n (1 + \frac{p}{100} - \frac{q}{100} - \frac{p q}{100^{2}}) / n 1 + \frac{p}{100} - \frac{q}{100} - \frac{p q}{100^{2}} = 1 \frac{p}{100} - \frac{q}{100} = \frac{p q}{100^{2}} \Rightarrow p - q = \frac{p q}{100}

Question 44. Ravi took a loan of Rs. 1 Lakh from SBI at the rate of

6 %

per annum of simple interest for 10 years. After some time, the rate of interest dropped down to

4 %

and as a result, Ravi paid only Rs. 1.48 lakhs at the end of the loan period. Number of years after which the rate of interest was decreased to

4 %

is___

Discuss Question

:
He paid Rs. 48,000 interest in 10 years.

\frac{48, 000}{1, 00, 000} \times 100 = 48 %

in 10 years. So,

4.8 %

in a year.

Ravi Took A Loan Of Rs. 1 Lakh From SBI At The Rate Of 6% ...

After 4 years the rate of interest was decreased to

4 %

Question 45. In an automated plant assembly line, the rate of rejection of components was

10 %

on July 1st and

6 %

on July 2nd. The combined rate of rejection for the two days was

9 %

. The ratio of production volumes on July 1st and on July 2nd is

2: 1
3: 2
3: 1
2: 5

Discuss Question

Answer: Option C. -> 3: 1
:
C
Use alligation

In An Automated Plant Assembly Line, The Rate Of Rejection O...

Answer is option (c)

Question 46. Sets A, B, C and D are all subsets of quadrilaterals. A is the set of rhombi, B is the set of rectangles, C is the set of parallelograms, and D is the set of kites. What is the set (A

\cap

\cup

\cap

D)?

squares
rectangles
parallelograms
rhombi

Discuss Question

Answer: Option D. -> rhombi
:
D
A

\cap

B is a set of quadrilaterals that are both rhombi and rectangles - which are squares. C

\cap

D is a set of quadrilaterals that are both parallelograms and kites - which are rhombi. Finally, the union of squares and rhombi are... rhombi.

Question 47. In a survey, 100 people were asked about their favourite Holiday spot in India among three places: Goa, Shimla or Kashmir. All the people had at least one of these three spots as their favourite one. 90 people named Goa as their favourite, 80 people named Shimla as their favourite and 80 people named Kashmir as their favourite.
Determine the maximum number of people who could have named all three places as their favourite.

Discuss Question

Answer: Option C. -> 75
:
C
C
For III to be the maximum, II = 0 III = 75

Question 48. 30% of the crowd at a mall is > 25 years and 80% of the crowd at the mall is <50 years. 20% of the crowd visits bantaloons. If 20% of the crowd above the age of 50 visit bantaloons, then what percentage of bantaloon visitors are < 50 years?

Discuss Question

Answer: Option D. -> 80%
:
D
20% of the crowd is above 50 years. 20% of this crowd visits bantaloons. Therefore 20% of 20% is 4% of the total crowd above 50 years visit bantaloons and therefore 16% of the crowd below the age of 50 years visit bantaloons.
20% of entire crowd visits bantloons
Therefore the % of crowd which visits bantaloons and below age of 50 =

\frac{16}{20} \times 100 = 80

Shortcut:
The given information can be carefully observed.
The crowd is divided into 2 groups: lesser than 50 and greater than 50. So the entire set can be made by adding both the groups.
Now the group that is greater than 50 forms 20% of the population that visit bantaloons, hence 80% of the crowd should be below the age of 50 and this is what has been asked.

Question 49. In an examination, 53 passed in Maths, 61 passed in Physics, 60 in Chemistry, 24 in Maths & Physics, 35 in Physics & Chemistry, 27 in Maths & Chemistry and 5 in none. Find the number of students who passed in all subjects if the total number of students who had appeared in the examination was 100.

Discuss Question

Answer: Option C. -> 7
:
C
X = I + II + III = 100 – 5 = 95 As 5 students have passed in none.
S = I + 2II + 3III = 53 + 61 + 60 = 174
S – X = II + 2III = 174 – 95 = 79 ... (i)
Number of people who have passed in two subject = 24 + 35 + 27 = 86 = II + 3III... (ii)
From (i) and (ii), III = 86 – 79 = 7
So, people who have passed in all three subjects = 7

Question 50. What is the total number of students who opted for only football?