Test: Linear Equations- 2 - Class 8 MCQ

3x=2x+18
3x-2x=18 (transposing)
x= 18

x = 4/5*(x + 10)

=> x = 4x/5 + 8

=> x - 4x/5 = 8

=> (5x - 4x)/5 = 8

=> x = 8 * 5 = 40

Verification / Checking-

LHS = x = 40

RHS = 4/5*(x + 10) = 4/5*(40 + 10) = 4/5 * 50 = 40

Given,

Sum of multiples of 7 = 357

Let the numbers be x, x + 7 , x + 14

ATP,

x + x + 7 + x + 14 = 357

3x + 21 = 357

3x = 357 - 21

3x = 336

x = 336/3

x = 112

Therefore,

the smallest multiple is x = 112 

Let the unit digit be y & tens digit be x.

Original number = (10x+y)

After interchanging the digits 

New number = (10y+x)

(10x+y) + (10y+x) = 110

11x +11y = 110

11(x+y)= 110

x+y = 110/11

x+y= 10          (1)

x= 10-y           (2)

(10x+y) - 10 = 4+ 5(x+y)

(10x+y) - 10 = 4+ 5(10)

(10x+y) = 4+ 50+10

(10x+y) = 64

10(10-y) +y = 64

100-10y +y= 64

100 -9y = 64

-9y = 64-100

-9y = -36

y= 36/9= 4

y= 4

putting the value of y in eqn 2

x= 10-y

x= 10-4

x= 6

Hence , the first number is 6 & second number is 4.

Original Number is 10x+y = 10* 6+4= 60+4= 64

X = 7 + 2

= 9

5t-3=3t-5
5t-3t=-5+3
2t=-2
which gives t=-1

ax+by=a-b
ax=a-b-by
x=(a-b-by)/a
bx-ay=a+b
substituting
b((a-b-by)/a)-ay=a+b
(ab-b²-b²y-a²y)/a=a+b
ab-b²-(b²+a²)y=a²+ab
-(b²+a²)y=a²+ab-ab+b²
y=-(a²+b²)/(a²+b²)
y= -1
substituting value of y
x=(a-b-b(-1))/a
x=a/a
x=1

5x+ 9 = 5 + 3x
5x - 3x = 5 - 9
2x = -4
x = -2

y + 3 = 10
y = 10 - 3
y = 7

Let the number be x.
So, the other number is (x + 15).
(x + 15) + x = 95
2x + 15 = 95
2x = 95 - 15
2x = 80
x = 40
So, the numbers are 40 and 55.

This says that any given equation says that it’s LHS is equal to RHS.

Let the time taken by man be x days

time taken by boys be y days

work done by 1 man in one day=1/x

work done by 1 boy in one day=1/y

8/x+12/y = 1/10     - eq 1

6/x+ 8/y = 1/14       - eq2

Let u = 1/x & v = 1/y

8u+ 12y = 1/10       - eq3

6u+8v = 1/14         - eq4

Multiplying eq3 by 2 & eq4 by 3 

16u+ 24y = 2/10    - eq5
18u+24v = 3/14      - eq6

subtract eq 5 & 6
-2u = -3/14+2/10
-2u = (-3×10 +2×14)/140

-2u = (-30+28)/140

-2u = -2/140

u = 1/140

put this value in eq 5

16u+ 24y = 2/10

16×1/140 +24y  = 1/5

4/35+24y = 1/5

24y = 1/5-4/35

24y = (1×7-4)/35

24y = (7-4)/35

24y = 3/35

y= 3/35×24

y= 1/280

u=1/x

1/140 = 1/x

x = 140

v = 1/y

1/280 = 1/y
y = 280

A man complete the work in 140 days
A boy can complete the work in 280 days