Solving Equations with Variable on Both Sides

Q. A bag contains 50p, 25p and 10p coins in the ratio 5: 9: 4, amounting to Rs. 206. The total number of coins in the bag is

1. 660
2. 700
3. 720

Q.

Solve this equation

$x=\frac{4}{5}(x+10)$

Q.

A number is divided into two parts, such that one part is 10 more than the other. If the two parts are in the ratio 5 : 3, find the number and the two parts.

1. The number = 35 and the two parts are 15 and 20.

2. The number = 45 and the two parts are 20 and 25.

3. The number = 50 and the two parts are 15 and 35.

4. The number = 40 and the two parts are 15 and 25.

Q.

A father is $30$ years older than his son. In $12$ years, the man will be three times as old as his son. Find their current ages.

Q.

Solve :

$\frac{(3x-2)}{4}-\frac{(2x+3)}{3}=\frac{2}{3}-x$

Q.

The denominator of a rational number is greater than its numerator by 3. If the numerator is increased by 7 and the denominator is decreased by 1, the new number becomes $\frac{3}{2}$. The original number is

1. 8/11

2. 7/10

3. 2/5

4. 5/8

Q.

Question 1(k) :

Solve:

$1\frac{1}{3}+3\frac{2}{3}$

Q. If $\frac{3x+5}{4}+1=\frac{x+3}{6}$, then the value of '$x$' is

1. 3
2. - 3
3. 6
4. - 6

Q.

In a two digit number, ten’s digit is twice the unit’s digit. The number formed by interchanging the digits is 36 less than the original number. Find the number.

1. 48

2. 84

3. 70

4. 72

Q. The ratio of zinc and copper in an alloy is $7:9$. It the weight of the copper in the alloy is $11.7$ kg, find the weight of the zinc in the alloy.

Q.

$\text{Solve for x:}$
$6(x+5)–4(x+1)=9(x+3)$

1. $-\frac{2}{7}$

2. $-\frac{1}{7}$

3. $-\frac{5}{7}$

4. 7

Q. Solve the following equation and verify the solution 5x+2-3(x+2)=-2(x+1)+5(x-2)

Q.

What is the product of 2x and 5x?

Q.

The value of x will be

1. 1
2. 2
3. 4
4. 8

Q.

Solve:
$\frac{5x-4}{6}=2+\frac{3x}{2}$

1. - 3

2. 4

3. - 4

4. 2

Q.

If length and breadth of a rectangle are 'x' cm and 'y' cm respectively, then find the perimeter of the rectangle.

1. (2x + y) cm

2. (x + 2y) cm

3. (2x + 2y) cm

4. (x + y) cm

Q.

Solve the equation $\frac{3}{x+1}=\frac{6}{5x-1}$.

1. 2

2. 1

3. 9

4. 3

Q.

Find the value of x in the equation $\frac{x(x-b)+x(x-a)}{(x-a)(x-b)}=2$.

1. $ab$

2. $\frac{a}{b}$

3. $\frac{2ab}{a+b}$

4. $2ab$

Q. Sum of the digits of a two digit number is $9$. When we interchange the digits, it is found that the resulting new number is greater than the original number by $27$. What is the two digit number?

1. $31$
2. $37$
3. $33$
4. $36$

Q. If the length and breadth of a rectangle are 'x' and 'y' respectively, perimeter of the rectangle will be

1. x + y
2. 2x + y
3. x + 2y
4. 2x + 2y

Q.

The sum of the ages of a father and his son is $60$ years . If the sons age is $30$ years less than the fathers age , find the age of the father .

Q.

Find the value of $x$ in $kx+a=mx+b$.

1. $\frac{b-a}{k-m}$

2. $\frac{a-b}{k-m}$

3. $\frac{k-m}{a-b}$

4. $\frac{m-k}{a-b}$

Q.

In an isosceles triangle ABC, the equal sides measure 4x - 1 and x + 5 units. The value of x is

1. 2
2. 1
3. - 2
4. - 1

Q. If x + 10 = 6
Find the value of x.

Q.

Value of m in the equation 9 + m = 6m + 8 - m is $\frac{1}{4}$

1. True

2. False

Q.

$\text{Solve for m:}$

$\frac{8m}{6}+5=7m$

1. $m=\frac{17}{15}$

2. $m=\frac{12}{17}$

3. $m=\frac{15}{14}$

4. $m=\frac{15}{17}$

Q.

The distance between P and Q along a river is 120km. The speed of the river current is 3km/hr from P to Q. A boat takes 10 hrs to travel from P to Q. Whal time will it take to return from Q to P ?

Q.

Sum of the digits of a two digit number is 9. When we interchange the digits the new number is 27 greater than the earlier number. Find the number. [3 MARKS]

Q.

A two-digit number is such that its product of its digit is $18$. When $63$ is subtracted from the number, the digits interchange their places. Find the number.

Q.

Rupas age becomes double the age of Shyam after 5 years. If Shyams present age is x years then what is Rupas age after 5 years?