1. Solve 15y = 10y-5 and verify the solution.

15y = 10y-5

15y-10y = -5

Verification

LHS = 15y = 15(-1) = -15

RHS = 10y-5 = 10 × (-1)-5

                       = -10-5 = -15

LHS = RHS

2. Solve 15x-1 = 2(5x-2)+8 and verify the solution.

15x-1 = 2(5x-2)+8

15x-1 = 10x-4+8

15x-10x = -4+8+1

          5x = 5

Verification

LHS = 15x-1

= 15×1-1 = 15-1 = 14

RHS = 2(5x-2)+8

=2(5-2)+8

=2×3+8 = 6+8 = 14

LHS = RHS

3. Solve and verify the solution.

LCM of 3, 4, 2 = 12

Multiply the given equation by 12

4(x+2)-3(x-3) = 60-6(x-1)

4x+8-3x+9 = 60-60x+6

4x-3x+6x = 60+6-8-9

Verification

4. A mother is 24 years older than her son. After 4 years, the age of mother will be three times the age of son. Find the present age of mother and son.

Let the age of son = x years

After 4 years, age of mother = 24+x+4

                                                 =x+28

                        age of son = x+4

Given that

x+28 = 3(x+4)

Present age of son = 8 years

      Present age of mother = 24+8 = 32 years

5. Kanshyap is 21 years old and Kinshuk is 15 years younger to Kanshyap. After how many years will Kanshyap be twice as old as Kinshuk?

Age of Kanshyap = 21 years

Age of Kinshuk     = 21-15 = 6 years

After x years, age of Kanshyap = 21+x and

                        age of Kinshuk    = 6+x

According to question,

6. The sum of digits of a 2 digit number is 7. The number obtained by interchanging the digits exceeds the original number by 27. Find the number

Let unit digit of a number = x

Let tens digit of a number =7-x

When the digits are inter changed

unit digit = 7-x and tens digit = x

New number = 10x+7-x

                           =9x+7

According to the question,

9x+7 = 70-9x+27

9x+9x = 70+27-7

18x = 90

Number = 70-9x

                    = 70-9×5 = 70-45

                                     =25

7. The ages of Suman and Neelam are in the ratio 3:4, 4 years ago, their ages were in the ratio 5:7. Find their ages.

Let the age of Suman = 3x and

Let the age of Neelam = 4x

4 years ago,

                       age of Suman = 3x-4

                       age of Neelam = 4x-4

By question,

                      ,

Age of Suman = 3x = 24 years

    Age of Neelam = 4x = 32 years

8. Solve

9. Solve

10. The difference between two positive integers is 51. The quotient when one integer is divided by the other is 4. Find the two integers.

Let the numbers are x and x-51

Given that

11. The ratio of two numbers is 3:5. If each number is increased by 10, the ratio between the numbers so formed is 5:7. find the two two original numbers.

Let the numbers be 3x and 5x.

If increased by 10, the numbers are 3x+10 and 5x+10

Given that

The numbers are 3×5 and 5×5, ie 15 and 25.