Solving an Equation with Variables on Both Sides

Q.

Solve the equation:$\frac{2x}{3}+1=\frac{7x}{15}+3$

Q.

A bag contains $25$ paise coins, $50$ paise coins and $1$ Rupee coins whose values are in the ratio of $8:4:2$ the total values of the coins are $840$. Find the total number of coins?

Q. A man can row at 5kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

1. 2.6 km
2. 3 km
3. 2.4 km
4. 3.6 km

Q.

A motorboat goes downstream in river and covers a distance between two coastal towns in 6 hours. It covers this distance upstream in 8 hours. If the speed of the stream is 2 km/hr, find the speed of the boat in still water. [4 MARKS]

Q. If a train travels at a speed of 50 kmph, it reaches its destination 10 minutes late. But if it travels at a speed of 60 kmph, it reaches its destination 5 minutes earlier. Find the distance covered to reach its destination.

1. 95 km
2. 85 km
3. 100 km
4. 75 km

Q. The time taken by a person to cover a certain distance on a motorboat when travelling downstream is 4 hours, while the same distance is covered in 5 hours upstream. If the speed of the stream is 2 kmph, then find the speed of the motorboat in still water.

1. 20 kmph
2. 16 kmph
3. 14 kmph
4. 18 kmph

Q. The present age of Rakesh is three times his age ten years ago. What was his age ten years ago?

1. 15
2. 20
3. 10
4. 5

Q. Question 4
Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

Q. 12 subtracted from nine times a number is equal to the sum of seven times the number and 4. What is the number?

1. 8
2. 12
3. 9
4. 7

Q. $\text{Find the value of 'p' for the equation,}2(p+5)=(p-1).$

1. 9
2. 10
3. -11
4. -10

Q. Half of the students in a class are dancing and three-fourths of the remaining students are playing cricket. If the remaining 9 students are studying in the library, then find the total number of students in the class.

1. 96
2. 84
3. 80
4. 72

Q.

Solve for $x$: $2x-\frac{17}{2}-(x-x-\frac{1}{3})=12$

Q. A man had to walk a certain distance. He covered one thirds of it at 5 kmph and the remaining distance at 6 kmph. If the total time taken is 40 minutes, then find the total distance.

1. 5.25 km
2. 3.75 km
3. 4 km
4. 6.5 km

Q. Find the value of $x$ in the following figure in order to make $AB\parallel CD$.

1. ${31}^{\circ }$
2. ${11}^{\circ }$
3. ${21}^{\circ }$
4. ${25}^{\circ }$

Q. Question 8
Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. Find these numbers.

Q. $\text{Solve for the value of t.}\frac{3t+1}{16}-\frac{3t-3}{7}=\frac{t-4}{8}+\frac{3t+1}{14}$

Q.

In the figure $x,y$ and $z$ are the internal angles of $△ABD.$ Line $ED\parallel AB$ and side $AD$ is extended to point $P$ and the value of $\angle EDP$ and $\angle EDB$ are $n$ and $m,$ respectively. Then, the values of $n$ and $m$ are ______ and _______, respectively.

1. z, y

2. x, z

3. y, z

4. y, x

Q. Half of the students in a class are dancing and three-fourths of the remaining students are playing cricket. If the remaining 9 students are studying in the library, then find the total number of students in the class.

1. 96
2. 84
3. 80
4. 72

Q. $\text{Solve for the value of t.}\frac{3t+1}{16}-\frac{3t-3}{7}=\frac{t-4}{8}+\frac{3t+1}{14}$

1. $\frac{13}{16}$
2. $\frac{-12}{16}$
3. $\frac{13}{8}$
4. $\frac{23}{65}$

Q. The present age of Hari’s mother is four times the present age of Hari. After 10 years, their ages will add to 80 years. Find their present ages.

1. 10, 40
2. 15, 45
3. 9, 36
4. 12, 48

Q. (a) Find the values of x in each of the following figures if l is parallel to m and a is parallel to b. [4 MARKS]


(b) What is the value of x in the figure?

Q. The numbers are in the ratio 4:3. If they differ by 18, find these numbers.
$\left[2Marks\right]$

Q.

Marks scored by Shveta are $10$ more than twice the marks scored by Reena. If Reena scored $x$marks , what are the Shvetas marks ?

Q.

Solve the following equation

$4(m+3)=18$

Q. Bitu is 26 years younger than her mother. If after 16 years, the ratio of their ages is 15:28, then Bitu's present age is .

1. 16
2. 14
3. 12
4. 18

Q. Rashni is 25 years older than her son Ankit. 20 years ago, Rashni was six times as old as Ankit. Find the present age of Ankit.

1. 20
2. 35
3. 25
4. 40

Q.

In the given figure, find \(\angle ADG\) and $\angle IEJ$. ABCD is a rectangle. [4 MARKS]

Q.

Subtracting $2xy$ from $-5xy$, we get ___________.

Q. Rima has ₹250 in ₹5 and ₹10 coins. If the number of ₹10 coins is twice the number of ₹5 coins, then find the number of ₹5 coins with her.

1. 20
2. 25
3. 15
4. 10

Q. Find the value of t which satisfies the following equation.
$6(t-2)+7(3-8t)=4(t-2)-4(4-t)$

1. $\frac{-11}{8}$
2. $\frac{11}{8}$
3. $\frac{4}{3}$
4. $\frac{33}{58}$