# Linear Equations – Part 1

1. The perimeter of a rectangle is 18cms and its width is 3.5cm. Find its length?

A.6.5cm

B.5.5cm

C.4.5cm

D.8.5cm

[su_spoiler title=”Answer” icon=”arrow-circle-2″]

Ans: (B)

Sol. Let the length be x cm

perimeter = 2(l+b)=2(x+3.5)cm

2x+7=18cm

2x=18-7

2x=11

x=11/2=5.5cm

[/su_spoiler]

2.Five times a number reduced by 10 is equal to three the number added to 8. Find the number.

A.10

B.9

C.8

D.11

[su_spoiler title=”Answer” icon=”arrow-circle-2″]

Ans: (B)

Sol. 5x-10=3x+8

5x-3x=8+10

2x=18

x=18/2=9

[/su_spoiler]

3. The present age of Surya’s father is 2 times the present age of surya. After 5 years their ages will add to 85years. Find their present ages.

A. 30yrs, 40yrs

B. 35yrs, 45yrs

C. 25yrs, 50yrs

D. 20yrs, 50yrs

[su_spoiler title=”Answer” icon=”arrow-circle-2″]

Ans: (C)

Sol. present age of surya=x father=2x sum

After 5yrs =x+5 =2x+5 3x+10

3x+10=85

3x=85-10

3x=75=25yrs

Father’s age=2x

2 x 25=50yrs

[/su_spoiler]

4. The difference between two whole numbers is 84. The ratio of the two numbers is 5:9. What are the numbers?

A. 96,194

B.104,180

C.105,189

D.84,184

[su_spoiler title=”Answer” icon=”arrow-circle-2″]

Ans: (C)

Sol. Let the numbers be 5x and 9x

9x-5x=84

4x=84

x=21

First numbers=5x= 5 x 21=105

Second number=9x= 9 x 21=189

[/su_spoiler]

5. Present age of siri and hari are in the ratio of 3:4. Four years from now the ratio of their ages will be 4:5. Find their present ages.

A.21yrs,23yrs

B.13yrs,23yrs

C.14yrs,16yrs

D.12yrs,16yrs

[su_spoiler title=”Answer” icon=”arrow-circle-2″]

Ans: (D)

Sol. Let the present age of siri and hari be 3x and 4x

Ratio of their ages after four years=3x+4/4x+4

But it is given as 4:5

therefore 3x+4/4x+4=4/5

4(4x+4) = 5(3x+4)

16x+16 = 15x+20

16x-15x = 20-16

1x = 4

Present age of siri =3x=3 x 4=12yrs

hari=4x=4 x 4=16yrs

[/su_spoiler]

6. Total strength of a school is 575. The number of boys is 2/3 the number of girls. Find the number of boys.

A.220

B.250

C.230

D.420

[su_spoiler title=”Answer” icon=”arrow-circle-2″]

Ans: (C)

Sol. Let the number of girls= x , number of boys= 2/3x

Total strength=575

x+2/3x=575

3x+2x/3 = 575 x 3

5x = 575 x 3

x=575 x 3/5=345 girls

number of boys=2/3 x 345=230

[/su_spoiler]

7. Anu’s age is two times the venu’s age. After five years the sum of their ages would be 28yrs. Find the present ages.

A.4yrs,8yrs

B.6yrs,12yrs

C.8yrs,16yrs

D.10yrs,20yrs

[su_spoiler title=”Answer” icon=”arrow-circle-2″]

Ans: (B)

Sol. Let Venu’s age be x yrs , Anu’s age =2x

After 5 years Venu’s age =x+5, Anu’s age (2x+5)

Sum of their ages= (x+5)+(2x+5)=3x+10

3x+10=28

3x=28-10

3x=18=6

x=6yrs , 2x=2 x 6=12yrs

[/su_spoiler]

8. The product two numbers is 1296. If one of them is 54, find the other?

A.64

B.48

C.36

D.24

[su_spoiler title=”Answer” icon=”arrow-circle-2″]

Ans: (D)

Sol. Let the other number be x

54 X x =1296

x=1296/54=24

[/su_spoiler]

9. Sum of two numbers is 86. One of the number is 8 more than the other. Find the numbers?

A. 64,22

B.50,42

C.47,39

D.25,61

[su_spoiler title=”Answer” icon=”arrow-circle-2″]

Ans: (C)

Sol. Let the 1^{st} number be x

2^{nd} number be x+8

Sum= x+(x+8)=86

2x+8=86

2x=86-8

2x=78

x=78/2=39, x+8=47

[/su_spoiler]

10. The perimeter of a square is 976mts. Find the side of the square?

A.284mts

B.254mts

C.244mts

D. 344mts

[su_spoiler title=”Answer” icon=”arrow-circle-2″]

Ans: (C)

Sol. Let the side of the square=x

perimeter = 4 x s

4s= 976

s=976/4=244mts

[/su_spoiler]