Solving Equation in One Variable

Q.

An equation_________ if the LHS and the RHS are interchanged.

Q. Prem and Manoj are partners in a firm sharing profits in the ratio of $3:2$. The Partnership Deed provided that Prem was to be paid salary of $Rs.2,500$ per month and Manoj was to get a commission of $Rs.10,000$ per year. Interest on capital was to be allowed @ 5% p.a. and interest on drawings was to be charged @ 6% p.a. Interest on Prem's drawings was $Rs.1,250$ and on Manoj's drawings was $Rs.425$. Interest on Capitals of the partners were $Rs.10,000$ and $Rs.7,500$ respectively. The firm earned a profit of $Rs.90,575$ for the year ended 31st March, 2018.
Prepare Profit and Loss Appropriation Account of the firm.

Q.

An __________remains the same, if the LHS and the RHS are interchanged.

Q. A can contains a mixture of two liquids $A$ and $B$ in the ratio $7:5.$ When $9$ litres of mixture are drawn off and the can is filled with $B,$ the ratio $A$ and $B$ becomes $7:9$. How many litres of liquid $A$ was contained by the can initially ?

1. $20$
2. $21$
3. $10$
4. $25$

Q.

The ratio of $225m$ to $5km$ is:

1. $9:200$

2. $3:500$

3. $4:300$

4. $7:100$

Q.

Pawan is a cashier in a bank. He has currency notes of denominations 2000, 500 and 100 respectively. The ratio of the number of these notes is 1:3:5. If the total cash with Pawan is Rs.5, 00, 000, how many notes of Rs.2000 denomination does he have?

1. 250

2. 375

3. 625

4. 125

Q. $A$ and $B$ are partners from 1st April, 2017, without a Partnership Deed and they introduced capitals of $Rs.35,000$ and $Rs.20,000$ respectively. On 1st October, 2017, $A$ advances a loan of $Rs.8,000$ to the firm without any agreement as to interest. The Profit and Loss Account for the year ended 31st March, 2018 shows a profit of $Rs.15,000$ but the partners cannot agree on payment of interest and on the basis of division of profits.
You are required to divide the profits between them giving reasons for your method.

Q.

Perimeter of a square plot with side 2$x$ is 40 units. Find the length of the side of the square plot.

1. 16 units

2. 5 units

3. 10 units

4. 20 units

Q. The ratio of the ages of Kim, Jim, and Tim is 4: 7: 5. The ratio of the ages of Tim, Dan, and Linda is 3 : 11 : 9. What is the ratio of ages of all the friends in the same order?

1. 4:7:5:11:9
2. 4:7:5:9:11
3. 12:21:15:45:55
4. 12:21:15:55:45

Q. If the sum of three consecutive multiples of 9 is 108, then the average of multiples is _______.

1. 56
2. 26
3. 46
4. 36

Q.

Fill in the blanks with $>,<$ or $=$

$\left(-4\right)+\left(-7\right)$____$\left(-4\right)-\left(-7\right)$

Q. Find the value of $x$ that satisfies the given equation.

$5x+10=26+x$

1. 4
2. 3
3. 15
4. 25

Q. Solve $2x+5=3(x+2)$ for $x$.

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

Q. ''5 decreased by 3x gives 3y'' is algebraically written as
5 - 3x = 3y.

1. True
2. False

Q.

The number $22$ has to $33$ the same ratio that ____ has to $24$.

Q. If $a+b=10$, then match the corresponding values of $b$
for a given value of $a$.

1. $b=9$
2. $b=0$
3. $b=7$
4. $b=5$

Q. In the equation 4(2x) = 60 - 12x, the value of x = .

1. 5
2. 3
3. 4

Q.

$\text{Solve the following equation for}x\text{.}$
$\frac{5x-4}{6}=2+\frac{3x}{2}$

1. 4

2. - 4

3. 2

4. - 3

Q. The number of terms that you get on simplifying (3x + 5)(x - 4) is

1. 2
2. 3
3. 4
4. 5

Q. The value of x in 2x-2= x is 2.

1. False
2. True