Solving Linear Equations Using Transpose of Terms

Q.

An express train takes $1\mathrm{hour}$ less than a passenger train to travel $132\mathrm{km}$ between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is $11\mathrm{km}/\mathrm{h}$ more than that of the passenger train, find the average speed of the two trains.

Q.

The denominator of a rational number is greater than its numerator by $8$.

If the numerator is increased by $17$ and the denominator is decreased by $1$, the number obtained is $\frac{3}{2}$.

Find the rational number.

Q.

How to integrate $e^{2x}$?

Q.

How to solve $8x+4=3\left(x-1\right)+7$ ?

Q.

Solve for x:
$\frac{x+5}{6}-\frac{x+1}{9}=\frac{x+3}{4}$

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

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

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

4. 7

Q.

Simplify and solve the following linear equation: $3(5z-7)-2(9z-11)=4(8z-13)-17$

Q.

Reema read $\frac{1}{5}$th pages of a book. If she reads further $40$ pages, she would have read $\frac{7}{10}$th pages of the book. How many pages are left to be read$?$

Q.

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

1. 72

2. 80

3. 84

4. 96

Q.

Solve: $5x-2(2x-7)=2(3x-1)+\frac{7}{2}$

Q.

If $y=1-x+\frac{x^2}{2!}-\frac{x^3}{3!}+\frac{x^4}{4!}-...$ then $\frac{d^{2}y}{d{x}^2}$is equal to

1. $-x$

2. $x$

3. $y$

4. $-y$

Q.

Solve :

$\frac{[2x-(7-5x\left)\right]}{[9x-(3+4x\left)\right]}=\frac{7}{6}$

Q.

The ages of two friends Ani and Biju differ by $3$year.

Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy.

The ages of Cathy and Dharam differ by $30$year.

Find the ages of Ani and Biju.

Q.

Solve the equation:

$\left|x-1\right|=1-x$

Q.

Solve the following:

$\frac{3x–8}{2x}=1$

Q.

If $P(n,r)=1680$ and $C(n,r)=70$ , then $69n+r!$ is equal to

1. $128$

2. $576$

3. $256$

4. $625$

5. $1152$

Q.

$\frac{(2-7x)}{(1-5x)}=\frac{(3+7x)}{(4+5x)}$. Solve for$x$.

Q.

The total number of three digit numbers, the sum of whose digits is even, is equal to

1. $450$

2. $350$

3. $250$

4. $325$

Q.

The real number $x$ when added to its inverse gives the minimum value of the sum at $x$ equal to

1. $-2$

2. $2$

3. $1$

4. $-1$

Q.

A number of friends decided to go on a picnic and planned to spend Rs. 96 on eatables. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs. 4 each extra. Find the number of those who attended the picnic.

Q. A man is $24$ years older than his son. In $2$ years, his age will be twice the age of his son. Find their present ages.

Q. If $45$ men can do a piece of work in $15$ days, in how many days will $9$ men do it?

1. $75$ days
2. $60$ days
3. $45$ days
4. $30$ days

Q. In a two digit number, digit at the tens place is twice the digit at units place. If the number obtained by interchanging the digits is added to the original umber, the sum is 66. Find the number.

1. 62
2. 24
3. 42
4. 26

Q. The sum of two consecutive multiples of 5 is 55. Find these multiples.

Q.

A motorboat whose speed is $24km/hr$ in still water takes $1hour$ more to go $32km$ upstream than to return downstream to the same spot. Find the speed of the stream.

Q.

Ravi walks at the uniform rate of $5km/hr$. What distance would he cover in $2$ hours $24$ minutes ?

Q.

Solve the following:

$4t–3–(3t+1)=5t–4$

Q.

Find the measure of an angle, if seven times its complement is ${10}^{\circ }$ less than three times its supplement.

Q.

The sum of two numbers is $30$ and their difference is $12$.

What are the $2$ numbers?

Q. In an orchard, $\frac{1}{5}$ are orange trees, $\frac{3}{13}$ are mango trees and the rest are banana trees. If the banana trees are $148$ in number, find the total number of trees in the orchard.

1. $252$
2. $360$
3. $260$
   
4. $352$

Q.

The average age of a husband and his wife was $23$ years at the time of their marriage. After five years, they have a one-year-old child. The average age of the family now is

1. $19$

2. $23$

3. $29$

4. $28$