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Test: Equations- 4

40 Questions MCQ Test Quantitative Aptitude for CA CPT | Test: Equations- 4

Description

Attempt Test: Equations- 4 | 40 questions in 40 minutes | Mock test for CA Foundation preparation | Free important questions MCQ to study Quantitative Aptitude for CA CPT for CA Foundation Exam | Download free PDF with solutions

QUESTION: 1

A number consists of two digits. The digits in the ten’s place is 3 times the digit in the unit’s place. If 54 is subtracted from the number the digits are reversed. The number is

A.
39
B.
92
C.
93
D.
94

Solution:

QUESTION: 2

The sum of the digits of a two digit number is 10. If 18 be subtracted from it the digits in the resulting number will be equal. The number is

A.
37
B.
73
C.
75
D.
none of these

Solution:

QUESTION: 3

Three persons Mr. Roy, Mr. Paul and Mr. Singh together have R.s 51. Mr. Paul has Rs. 4 less than Mr. Roy and Mr. Singh has got Rs. 5 less than Mr. Roy. They have the money as.

A.
(Rs. 20, 16, 15)
B.
(Rs. 15, 20, 16)
C.
(Rs. 25, 11, 15)
D.
none of these

Solution:

QUESTION: 4

One student is asked to divide a half of a number by 6 and other half by 4 and then to add the two quantities. Instead of doing so the student divides the given number by 5. If the answer is 4 short of the correct answer then the number was

A.
320
B.
400
C.
480
D.
none of these

Solution:

QUESTION: 5

Monthly incomes of two persons are in the ratio 4:5 and their monthly expenses are in the ratio 7:9. If each saves Rs. 50 per month find their monthly incomes.

A.
(500, 400)
B.
(400, 500)
C.
(300, 600)
D.
(350, 550)

Solution:

QUESTION: 6

The simultaneous equations 7x-3y=31, 9x-5y=41 have solutions given by

A.
(-4, -1)
B.
(-1, 4)
C.
(4, -1)
D.
(3, 7)

Solution:

QUESTION: 7

2x+3y+4z=0, x+2y-5z=0, 10x+16y-6z=0

A.
(0, 0, 0)
B.
(1, -1, 1)
C.
(3, 2, -1)
D.
(1, 0, 2)

Solution:

QUESTION: 8

1.5x+3.6y=2.1, 2.5(x+1)=6y

A.
(0.2, 0.5)
B.
(0.5, 0.2)
C.
(2, 5)
D.
(-5, -2)

Solution:

QUESTION: 9

3x-4y+70z=0, 2x+3y-10z=0, x+2y+3z=13

A.
(1, 3, 7)
B.
(1, 7, 3)
C.
(2, 4, 3)
D.
(-10, 10, 1)

Solution:

QUESTION: 10

Find the fraction which is equal to 1/2 when both its numerator and denominator are increased by 2. It is equal to 3/4 when both are increased by 12.

A.
3/8
B.
5/8
C.
2/8
D.
2/3

Solution:

QUESTION: 11

If ?? be the roots of the equation 2x²-4x-3=0 the value of ?²+?² is

A.
5
B.
7
C.
3
D.
-4

Solution:

QUESTION: 12

The wages of 8 men and 6 boys amount of Rs. 33. If 4 men earn Rs. 4.50 more then 5 boys determine the wages of each man and boy.

A.
(Rs. 1.50, Rs. 3)
B.
(Rs. 3, Rs.1.50)
C.
(Rs. 2.50, Rs. 2)
D.
(Rs. 2, Rs. 2.50)

Solution:

QUESTION: 13

Two numbers are such that twice the greater number exceeds twice the smaller one by 18 and 1/3 of the smaller and 1/5 of the greater number are together 21. The numbers are:

A.
(36, 45)
B.
(45, 36)
C.
(50, 41)
D.
(55, 46)

Solution:

Let greater number is 'x'
Smaller number be 'y
Given,greater number exceeds twice the smaller i.e 2x-2y=18...........1
1/3 of smaller and 1/5 of greater i.e 1/3×y+1/5×x=21 this is convert as 3x+5y=315......2
By solving 1 and 2 we get x=45 and y=36

QUESTION: 14

If the roots of the equation 2x²+8x-m³=0 are equal then value of m is

A.
-3
B.
-1
C.
1
D.
-2

Solution:

QUESTION: 15

A number between 10 and 100 is five times the sum of its digits. If 9 be added to it the digits are reversed find the number.

A.
54
B.
53
C.
45
D.
55

Solution:

QUESTION: 16

Of two numbers, 1/5^th of the greater is equal to 1/3^rd of the smaller and their sum is 16. The numbers are:

A.
(6, 10)
B.
(9, 7)
C.
(12, 4)
D.
(11, 5)

Solution:

QUESTION: 17

The sum of the digits in a three digit number is 12. If the digits are reversed the number is increased by 495 but reversing only of the ten

A.
327
B.
372
C.
237
D.
273

Solution:

QUESTION: 18

The age of a person is twice the sum of the ages of his two sons and five years ago his age was thrice the sum of their ages. Find his present ages.

A.
60 years
B.
52 years
C.
51 years
D.
50 years.

Solution:

QUESTION: 19

Y is older than x by 7 years 15 years back x's age was 3/4 of y's age. There present age are

A.
(X=36, Y=43)
B.
(X=50, Y=43)
C.
(X=43, Y=50
D.
(X=40, Y=47)

Solution:

Y is older than X by 7 years:
Y=X+7
Y-X=7( this is equation 1)

15 years back X's age was 3/4th of Y's age:
(3/4)*(Y-15)=X-15
3(Y-15)=4(X-15)
3Y-45=4X-60
3Y-4X=-60+45
3Y-4X=-15 ( this is equation 2)

Solve both equations by simultaneous linear equation
Method:

Y-X=7( multiply by 3)
3Y-4X=-15

3Y-3X=21
3Y-4X=-15

X=36
Put X value in equation 1
And we will get Y=43

Therefore (36,43) is the answer.

QUESTION: 20

A number consisting of two digits is four times the sum of its digits and if 27 be added to it the digits are reversed. The number is

A.
63
B.
35
C.
36
D.
60

Solution:

QUESTION: 21

The roots of the equation x²+(2p-1)x+p²=0 are real if.

A.
P=1
B.
p=4
C.
p=1/4
D.
NONE

Solution:

QUESTION: 22

If 2^2x+3-3². 2^x+1=0 then values of x are

A.
0,1
B.
1, 2
C.
0, 3
D.
0, -3

Solution:

QUESTION: 23

If x=m is one of the solutions of the equation 2x²+5x-m=0 the possible values of m are

A.
(0, 2)
B.
(0, -2)
C.
(0, 1)
D.
(1, -1)

Solution:

QUESTION: 24

The values of x for the equation x²+9x+18=6-4x are

A.
(1, 12)
B.
(-1, -12)
C.
(1, -12)
D.
(-1, 12)

Solution:

QUESTION: 25

If the root of the equation x²-8x+m=0 exceeds the other by 4 then the value of m is

A.
m=10
B.
m=11
C.
m=9
D.
m=12

Solution:

QUESTION: 26

A solution of the quadratic equation (a+b-2c)x² + (2a-b-c)x + (c+a-2b)=0 is

A.
x=1
B.
x=-1
C.
x=2
D.
x=-2

Solution:

QUESTION: 27

If one rot of 5x²+13x+p=0 be reciprocal of the other then the value of p is

A.
-5
B.
5
C.
1/5
D.
-1/5

Solution:

QUESTION: 28

If L+M+N=0 and LMN are rationales the roots of the equation (M+N-L)x²+(N+L-M)x+(L+M-N)=0 are

A.
Real and irrational
B.
Real and rational
C.
Imaginary and equal
D.
Real and equal

Solution:

QUESTION: 29

The values of x in the equation 7(x+2p)²+5p²=35xp+117p² are

A.
(4p, -3p)
B.
(4p, 3p)
C.
(-4p, 3p)
D.
(-4p, -3p)

Solution:

QUESTION: 30

If p and q are the roots of x²+2x+1=0 then the values of p³+q³ becomes

A.
2
B.
-2
C.
4
D.
-4

Solution:

QUESTION: 31

The solution of the cubic equation x³-6x²+11x-6=0 is given by the triplet:

A.
(-1, 1, -2)
B.
(-2, 2, 3)
C.
(1, 2, 3)
D.
(0, 4, -5)

Solution:

x^3–6x^2+11x-6
=x^3-x^2–5x^2+5x+6x-6
=x^2(x-1)-5x(x-1)+6(x-1)
=(x-1)(x^2–5x+6)
=(x-1)(x^2–2x-3x+6)
=(x-1){x(x-2)-3(x-2)}
=(x-1){(x-2)(x-3)}
=(x-1)(x-2)(x-3)

Final solutions are

x=1, x=2, x=3

x1=1,x2=2,x3=3

QUESTION: 32

The sides of an equilateral triangle are shortened by 12 units 13 units and 14 units respectively and a right angle triangle is formed. The side of the equilateral triangle is

A.
17 units
B.
16 units
C.
15 units
D.
18 units

Solution:

QUESTION: 33

The area of a rectangular field is 2000 sq.m and its perimeter is 180m.Form a quadratic equation by taking the length of the field as x and solve it to find the length and breadth of the field. The length and breadth are

A.
(205m, 80m)
B.
(50m, 40)
C.
(40m, 50m)
D.
none

Solution:

QUESTION: 34

There are two consecutive numbers such that the difference of their reciprocals is 1/240. The numbers are

A.
15,16
B.
17, 18
C.
13, 14
D.
12, 13

Solution:

QUESTION: 35

Two squares have sides p cm and (p+5) cms. The sum of their squares is 625 sq. cm. The sides of the squares are

A.
(10cm, 30cm)
B.
(12cm, 25cm)
C.
(15cm, 20cm)
D.
none of these

Solution:

QUESTION: 36

The sum of two numbers is 8 and the sum of their squares is 34. Taking one number as x form an equation in x and hence find the numbers. The numbers are

A.
(7, 10)
B.
(4, 4)
C.
(3, 5)
D.
(2, 6)

Solution:

QUESTION: 37

A distributor of apple juice has 5000 bottle in the store that it wishes to distribute in a month. From experience it is known that demand D (in number of bottles) is given by D= -2000p²+2000p+17000. The price per bottle that will result zero inventory is

A.
Rs. 3
B.
Rs. 5
C.
Rs. 2
D.
none of these

Solution:

QUESTION: 38

The difference of two positive integers is 3 and the sum of their squares is 89. Taking the smaller integer as x form a quadratic equation and solve it to find the integers. The integers are