Q.1 The perimeter of a rectangular park is 200m . Its length is 10 m more than twice its breadth . What is the length and breadth of the park?

Solution: Let the breadth of the park is x metres

Then, Length =(2x+10) Metres

Perimeter of park=200m

∴ 2(2x+10+x)=200

2(3x+10)=200

6x+20=200

6x=180

x=30

So,Breadth of park is 30 m

Length of park =(2x+10) Metres ={(2×30)+10}={60+10}=70

Q.2 A number is such that ratio of 84 less than the number and difference of 108 and the number is 1:1. Find the number and verify your answer

Solution: Let the required number is x

84 less than the number =x-84

Difference of 108 and required number =108-x

According to question ,

\frac{x-84}{108-x}=\frac{1}{1}

x-84=108-x

x+x=108+84

2x=192

x=96

So, Required number is 96

Q.3 Seema had 180 Rs with her in the form of 2 Rs and 5 Rs coins.The number of 2 Rs coins is twice the Number of 5 Rs coins.Find the number of coins of each type

Solution: Let the number of 5Rs coins is x

∴ The number of 2 Rs coins is 2x

The total amount of money=180

Amount of money in the form of 5 Rs coins =5Rs ×x

Amount of money in the form of 2 Rs coins = 2 Rs × 2x

According to the question,

5x+2(2x)=180

5x+4x=180

9x=180

x=20

So, Number of 5 Rs coins =x=20

Number of 2 Rs coins =2x=2×20=40

Q.4 The sum of the two numbers is 11 and their product is 30 .Find the numbers

Solution: Let one number is x

∴ Another number=11-x

It is given that ,their product is 30

x(11-x)=30

11x-x^{2}=30

x²-11x+30=0

x²-6x-5x+30=0

x(x-6)-5(x-6)=0

(x-6)(x-5)=0

(x-6)=0 or (x-5)=0

x=6 or x=5

So, Numbers are 6 and 5

Q.5 The denominator of a rational number is 1 more than the numerator . If the numerator is reduced by 2 and the denominator is increased by 3, the rational number reduces to \frac{1}{4}. Find the rational number

Solution: Let the numerator of a rational number is x

Denominator =(x+1)

So, Rational number =\frac{x}{x+1}

If the numerator reduced by 2 ,it becomes =(x-2)

and Denominator =(x+1)+3=x+4

New rational number = \frac{x-2}{x+4}

According to question,

\frac{x-2}{x+4}=\frac{1}{4}

4(x-2)=1(x+4)

4x-8=x+4

3x=12

x=4

Hence ,Required rational number is \frac{x}{x+1}=\frac{4}{5}