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This mock test of Test: Equations- 4 for CA Foundation helps you for every CA Foundation entrance exam.
This contains 40 Multiple Choice Questions for CA Foundation Test: Equations- 4 (mcq) to study with solutions a complete question bank.
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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

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

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 2x^{2}-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 2x^{2}+8x-m^{3}=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, 1/5^{th} of the greater is equal to 1/3^{rd} 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

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

Solution:

QUESTION: 21

The roots of the equation x^{2}+(2p-1)x+p^{2}=0 are real if.

Solution:

QUESTION: 22

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

Solution:

QUESTION: 23

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

Solution:

QUESTION: 24

The values of x for the equation x^{2}+9x+18=6-4x are

Solution:

QUESTION: 25

If the root of the equation x^{2}-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)x^{2} + (2a-b-c)x + (c+a-2b)=0 is

Solution:

QUESTION: 27

If one rot of 5x^{2}+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)x^{2}+(N+L-M)x+(L+M-N)=0 are

Solution:

QUESTION: 29

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

Solution:

QUESTION: 30

If p and q are the roots of x^{2}+2x+1=0 then the values of p^{3}+q^{3} becomes

Solution:

QUESTION: 31

The solution of the cubic equation x^{3}-6x^{2}+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= -2000p^{2}+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

Solution:

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