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Answer 1

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16) x = 9

17) Length = 25cm, breadth = 18 cm.

18) Reena = 17 years, Brother = 11 years.

19) Rahim's age = 18 years.

20 (i) m = - 54

20 (ii) m = 9

21 (i) 25 : 2

21 (ii) 25 : 23

21 (iii) 23 : 2

Step-by-step explanation :

16) 3 ( x + 3 ) - 2 ( x - 1 ) = 5 ( x - 5 )

⇒ 3x + 9 - 2x + 2 = 5x - 25

⇒ x + 11 = 5x - 25

⇒ 5x - x = 25 + 11

⇒ 4x = 36

⇒ x = 36 / 4

⇒ x = 9

Check your result ;

Putting the value of x, we get ;

3 ( x + 3 ) - 2 ( x - 1 ) = 5 ( x - 5 )

⇒ 3 ( 9 + 3 ) - 2 ( 9 - 1 ) = 5 ( 9 - 5 )

⇒ 3 * 12 - 2 * 8 = 5 * 4

⇒ 36 - 16 = 20

⇒ 20 = 20

Hence, the value of x is 9.

_______________________

17)

Length of wire = Perimeter of rectangle

Now,

Let the breadth of rectangle be x cm and length of rectangle be ( x + 7 ) cm.

According to the question,

Perimeter of rectangle = 86 cm

⇒ 2 ( l + b ) = 86

⇒ 2 ( x + 7 + x ) = 86

⇒ ( 2x + 7 ) = 86 / 2

⇒ 2x + 7 = 43

⇒ 2x = 43 - 7

⇒ 2x = 36

⇒ x = 36 / 2

⇒ x = 18

Now,

Breadth of rectangle = 18 cm.

Length of rectangle = x + 7

= 18 + 7

= 25 cm.

_______________________

18) Let the age of Reena's brother be x.

Then, Reena's age = ( x + 6 )

According to question,

⇒ x + x + 6 = 28

⇒ 2x + 6 = 28

⇒ 2x = 28 - 6

⇒ 2x = 22

⇒ x = 22 / 2

⇒ x = 11

Reena's brother's age = 11 years.

Age of Reena = x + 6

= 11 + 6

= 17 years

_______________________

19) Let the present age of Rahim be x.

After 32 years, his age be ( x + 32 ) years.

And, 8 years ago, his age = ( x - 8 ) years.

According to the question,

x + 32 = 5 ( x - 8 )

⇒ x + 32 = 5x - 40

⇒ 5x - x = 40 + 32

⇒ 4x = 72

⇒ x = 72 / 4

⇒ x = 18

The present age of Rahim is 18 years.

_______________________

20)

$\begin{gathered}\sf (i) \: \frac{2m}{3} + 8 = \frac{m}{2} - 1 \\ \\ \implies \sf \frac{2m}{3} - \frac{m}{2} = - 1 - 9 \\ \\ \implies \sf \frac{4m - 3m}{6} = - 9 \\ \\ \implies \sf \frac{m}{6} = - 9 \\ \\ \implies \sf m = - 9 \times 6 \\ \\ \therefore \underline{ \bf m = - 54}\end{gathered}$

_______________________

20)

$\begin{gathered}\sf (ii) \: \frac{3}{4} (x - 1) = (x - 3) \\ \\ \implies \sf \frac{3}{4} x - \frac{3}{4} = x - 3 \\ \\ \implies \sf \frac{3x - 3}{4} = x - 3 \\ \\ \implies \sf 3x - 3 = 4x - 12 \\ \\ \implies \sf 3x - 4x = - 12 + 3 \\ \\ \implies \sf \cancel - x = \cancel - 9 \\ \\ \therefore \underline{ \bf x = 9}\end{gathered}$

_______________________

21) Rohit's Earnings = Rs 15300

Rohit's Saving = Rs 1224

⇒ Expenditure = Rs ( 15300 - 1224 )

⇒ Expenditure = Rs 14076

(i) Ratio of his income and savings,

⇒ Ratio = Income / Saving

⇒ Ratio = 15300 / 1224

⇒ Ratio = 25 / 2

⇒ Ratio = 25 : 2

(ii) Ratio of his income and expenditure

⇒ Ratio = Income / expenditure

⇒ Ratio = 15300 / 14076

⇒ Ratio = 25 / 23

⇒ Ratio = 25 : 23

(iii) Ratio of his expenditure and saving

⇒ Ratio = expenditure / Saving

⇒ Ratio = 14076 / 1224

⇒ Ratio = 23 / 2

⇒ Ratio = 23 : 2

_______________________

Thanks for the question!

Answer 2

19. Let the present age of Rahim be x years.

After 32 years:

Rahim's age = (x + 32) years

8 years ago:

Rahim's age = (x 8) years

According to the question:

x + 32 = 5(x 8)

or, x + 32 = 5x 58

or, x + 32 = 5x 40

or, 40 + 32 = 5x x [Transposing 'x' to the R.H.S. and 40 to the L.H.S.]

or, 72 = 4x

or, [Dividing both the sides by 4]

or, x = 18

Thus, the present age of Rahim is 18 years.

18. Let the present age of Ajay be x years.

Since Reena is 6 years older than Ajay, the present age of Reena will be (x+ 6) years.

According to the question:

x + (x + 6) = 28

or, 2x + 6 = 28

or, 2x + 6 6 = 28 6 [Subtracting 6 from both the sides]

or, 2x = 22

or, [Dividing both the sides by 2]

or, x = 11

∴ Present age of Ajay = 11 years

Present age of Reena = x +6 = 11 + 6

= 17 years

21. Rohit's income = Rs 15300

Rohit's savings = Rs 1224

(i) Income:Savings = 15300:1224 = 15300 ​÷ 612 = 25 (H.C.F. of 15300 and 1224 is 612.)

1224 ​÷ 612 2

Income:Savings = 25:2

(ii) Monthly expenditure = Rs (15300 1224) = Rs 14076

Income:Expenditure = 15300:14076 = 15300 ÷ 612 = 25 (H.C.F. of 15300 and 14076 is 612.)

14076 ​÷ 612 23

Income:Expenditure = 25:23

(iii) Expenditure : Savings = 14076:1224 = 14076 ÷ 612 = 23 (H.C.F. of 14076 and 1224 is 612.)

1224 ​÷ 612 2

Expenditure:Savings = 23:2

17. Let the breadth of the rectangle be x cm.

Then, the length of the rectangle will be (x + 7) cm.

Perimeter of the rectangle = 2(Length + Breadth) = 2( x + 7 + x) cm

Given perimeter of the rectangle = Length of the wire = 86 cm



∴ 2( x + 7 + x) = 86

or, 2 ( 2x + 7 ) = 86

or, 2 ×2x + 2 × 7 = 86 [On expanding the brackets]

or, 4x + 14 = 86

or, 4x + 14 - 14 = 86 - 14 [Subtracting 14 from both the sides]

or, 4x = 72

or, [Dividing by 4 on both the sides]

or, x = 18 metres

Breadth of the hall = x

= 18 metres

Length of the hall = x + 7

= 18 + 7

= 25 metres

Only these I now and rest two questions my answer is coming wrong
So it is better to not put

Hope you like it

Or you can google rest two answers

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