Question

$\huge \fbox {Question}$
1.The perimeter of a rectangular swimming pool is 154 m. Its length is 2 m more than twice its breadth. What are the length and the breadth of the pool?
2.Sum of two numbers be 95. If one exceeds the other by 15, find the numbers.
3. Three consecutive integers add up to 51. What are these integers?
4.The ages of Rahul and Haroon are in the ratio 5 : 7. Four years later the sum of their ages will be 56 years. What are their present ages?
5. Two numbers are in the ratio 5 : 3. If they differ by 18, what are the numbers?

Answer 1

Answer:

1.Let the breadth be 'x'

Length=2+2x

The Perimeter of the rectangle =2(l+b)

By the given condition,

2(l+b)=154 m

2(2+2x+x)=154

2(2+3x) =154

4+6x=154

6x =154-4

=150

x =150/6

=25 m

Therefore, Breadth of the pool=25 m

Length of the pool=2+2×25=52 m

2.Let the bigger number be 'x' and smaller number be 'y'.

Given, x+y=95. . (1) and x-y=15. . (2)

∴ x=15+y. . (3)

Substitute this value of x in equation (1)

We get,

15+y+y=95

15+2y=95

2y=95-15

2y=80

y=80/2

=40

Put the value of y in equation (2) we get,

x-40=15

x=40+15=55

∴The two numbers are 40 and 55.

OR

Let the first number be 'x' and second number be 'x+15'.

x+x+15=95

2x+15=95

2x=95-15

2x=80

x=80/2

x=40

3.Let the three consecutive integers be x, x+1 and x+2

x+(x+1)+ (x+2) =51

3x+3=51

3x=51-3

3x=48

x=48/3

x=16

∴ The numbers are 16,17(x+1) and 18(x+2).

5.Let The two numbers be 5x and 3x

Since two numbers differ by 18, we can write the equation

5x – 3x = 18

2x = 18

x= 9

Therefore the two numbers are

5x = 5 x 9 = 45

and

3x = 3 x 9 = 27

∴ The two numbers are 45 and 27.

Answer to (4) is attached~

Hope this Helps:)

Answer 2

Answer:

Answer (1)

Given :-

• Perimeter of rectangle = 154
• Length is 2 m more than breadth

To Find :-

Length and breadth

Solution :-

Let the breadth be x m

Hence Length will be 2x + 2 m

$\tt \: 154 = 2(2x + 2 + x)$

$\tt \: 154 = 4x + 4 + 2x$

$\tt \: 154 = 6x + 4$

$\tt \: 154 - 4 = 6x$

$\tt \: 150 = 6x$

$\tt \: x = \cancel\dfrac{150}{6} = 25$

Length = 2x + 2 = 2 × 50 + 2 = 52

Breadth = x = 25 m

Answer (2)

Given :-

• Sum of two numbers = 95
• One exceeds 15 by other

To Find :-

Numbers

Solution :-

Let the smaller number be x

$\tt \: 95 = x + 15 + x$

$\tt \: 95 = 2x + 15$

$\tt \: 95 - 15 = 2x$

$\tt \:80 = 2x$

$\tt \: x = \frac{80}{2}$

$\tt \: x = 40$

One number = 40

Another number = 40 + 15 = 55

Answer (3)

Given :-

• Sum of three consecutive integer= 51

To Find :-

Integers

Solution :-

Let the consecutive integer be x,x+1,x+2

$\tt \: 51 = x + x + 1 + x + 2$

$\tt \: 51 = 3x + 3$

$\tt \: 51 - 3 = 3x$

$\tt \: 48 = 3x$

$\tt \: x = \dfrac{48}{3}$

$\tt \: x = 16$

Integers are :-

x = 16

x + 1 = 17

x + 2 = 18

Answer (4)

Given :-

• Age of Rahul and Haroon are in ratio 5:7
• After 4 years their sum of ages will be 56

To Find :-

Present age

Solution :-

Let the present age be 5x and 7x

$\tt \: (5x + 4) + (7x + 4) = 56$

$\tt \: 5x + 4 + 7x + 4 = 56$

$\tt \: 12x + 8 = 56$

$\tt \: 12x = 56 - 8$

$\tt \: 12x = 48$

$\tt \: x = \dfrac{48}{12} = 4$

Rahul age = 5x = 5(4) = 20 years

Haroon Age = 7x = 7(4) = 28 years

Answer (5)

Given :-

• Two numbers are in ratio 5:3
• They differ by 18

To Find :-

Numbers

Solution :-

Let the ratio be 5x and 3x

$\tt \: 5x - 3x = 18$

$\tt \: 2x = 18$

$\tt \: x = \dfrac{18}{2}$

$\tt \: x \: = 9$

Numbers are

5x = 5(9) = 45

3x = 3(9) = 27