Question

1. Find the solution of 3x-4 = 12 2. Solve: 5x-9 = 8 3. What should be subtracted from thrice the rational number -8/3 to get 5/2? 4. The sum of three consecutive multiples of 7 is 63. Find these multiples. 5. Solve 3x/4 – 7/4 = 5x + 12 6. Perimeter of a rectangle is 13cm. if its width is 11/4 cm, find its length. 7. The present of Sita’s father is three times the present age of Sita. After six years sum of their ages will be 69 years. Find their present ages. 8. The digits of a two-digit number differ by 3. If digits are interchanged and the resulting number is added to the original number, we get 121. Find the original number. 9. (x-2)/(x+1) = ½. Find x 10. Sanjay will be 3 times as old as he was 4 years ago after 18 years. Find his present age. 11. If the sum of two numbers is 30 and their ratio is 2/3 then find the numbers. 12. The numerator of a fraction is 2 less than the denominator. If one is added to its denominator, it becomes 1/2 find the fraction.


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Answer 1

1 )   3x – 4 = 12

=> 3x = 12 + 4

=> 3x = 16

=> x = 16/3 = 5 1/3 [ 5 × 3 + 1  = 16 ]

2 )   5x – 9 = 8

=> 5x = 8 + 9

=> 5x = 17

=> x = 17/5 = 3 2/5 [ 3 × 5 + 2 = 17 ]

3 )   -8/3 + 5/2

=> ( -16 + 15 ) / 6

=> –1/6

Hence , –1/6 should be subtracted from thrice the rational number -8/3 to get 5/2 .

4 ) Let the three consecutives be x , x + 7 , x + 14

A.T.Q.

x + x + 7 + x + 14 = 63

=> 3x + 21 = 63

=> 3x = 42

=> x = 42/3 = 14

Hence, the three consecutives are 14 , 21 , 28 .

x = 14

x + 7 = 14 + 7 = 21

x + 14 = 14 + 14 = 28

5 )  3x/4 – 7/4 = 5x + 12

=> 3x/4 – 5x/1 = 12/1 + 7/4

=> ( 3x – 20x )/4 = ( 48 + 7 )/4

=> –17x/4 = 55/4  ( 4 canceled  as the bases are equal )

=> x = 55/–17

6) P = 13cm

P = 2 ( L + b )

=> 13 = 2 ( L + 11/4 )

=> 13 = 2L + 11/2

=> ( 13 – 11 )/2 = 2L

=> ( 26 – 11 ) / 2 = 2L

=> 15/2 = 2L

=> L = 15 cm

7) Present age of sita = x

then present age of her father = 3x

and

(x+6)+(3x+6)=69

⇒4x+12=69

⇒4x=57

⇒x=457=14 1/4 years.

=14 3/12 years.

x=14 years and 3 months 

= sita's present age.

∴ present age of her father =3x

=42 years and 9 months.

8 ) Let us take the two digit number such that the digit in the units place is x. The digit in the tens place differs from x by 3. Let us take it as x + 3 So the two-digit number is

10(x + 3) + x = 10x + 30 + x = 11x + 30 .

With interchange of digits, the resulting two-digit number will be 10x + (x + 3) = 11x + 3 If we add these two two-digit numbers, their sum is

(11x+30)+(11x+3)=11x+11x+30+3=22x+ 33

It is given that the sum is 121.

Therefore, 22x + 33 = 121

22x = 121 - 33

22x = 8

x = 4

The units digit is 4 and therefore the tens digit is 4+3=7.

Hence, the number is 74 or 47.

9) (x-2)/(x+1) = ½

=> 2 ( x – 2 ) = 1 ( x + 1 )

=> 2x – 4 = x + 1

=> 2x – x = 1 + 4

=> x = 5

10) Let Sanjay's age be x

3(x - 4) = x + 18

3x - 12 = x + 18

3x - x = 18 + 12

2x = 30

x = 30/2

x = 15 years

the present age of Sanjay is 15 years .

11) Sum of two Ser = 30

Ratio=2/3 => 2x+3x (Here x is a variable

2x + 3x = 30

5x = 30

x=30/5

=>6

So numbers are

2x =2 × 6 => 12

3x =3 × 6 => 18

So , those two numbers are 12 and 18 .

12) Let the numerator be x

Denominator =x+2

When 1 is added to Denominator:

minator = x + 2 + 1 = x + 3

A.T.Q.

(x) / (x + 3) = 1/2

Cross multiplying

x + 3 = 2x

2x - x = 3

x = 3

Original Trator= underline x =3

Original Denominator Tr=x+2=3+2=5

Original fraction = 3/5

Verification:

Fraction =3/5

1 is added to the Denominator:

3 / (5 + 1) = 1/2

3/6 = 1/2

1/2 = 1/2

Hence verified

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