Test: Equations- 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 

 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. 

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

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

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

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

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.

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

 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.

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: 

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

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.

 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: 

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

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. 

 Y is older than x by 7 years 15 years back X

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

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

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

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

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

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

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

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

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

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

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

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

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 

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

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

 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

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 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

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 

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

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