# Test: Equations- 4

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

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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

Solution:
QUESTION: 2

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.

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

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.

Solution:
QUESTION: 6

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

Solution:
QUESTION: 7

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

Solution:
QUESTION: 8

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

Solution:
QUESTION: 9

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

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.

Solution:
QUESTION: 11

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

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.

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:

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

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.

Solution:
QUESTION: 16

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

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

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.

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

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

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

Solution:
QUESTION: 21

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

Solution:
QUESTION: 22

If 22x+3-32. 2x+1=0 then values of x are

Solution:
QUESTION: 23

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

Solution:
QUESTION: 24

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

Solution:
QUESTION: 25

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

Solution:
QUESTION: 26

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

Solution:
QUESTION: 27

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

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

Solution:
QUESTION: 29

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

Solution:
QUESTION: 30

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

Solution:
QUESTION: 31

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

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

Or

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

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

Solution:
QUESTION: 34

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

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

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

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

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

Solution:
QUESTION: 39

The sum of two numbers is 45 and the mean proportional between them is 18. The numbers are

Solution:
QUESTION: 40

Divide 50 into two parts such that the sum of their reciprocals is 1/12. The numbers are

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