Question 1 : If $x$ and $y$ are the two digits of the number $653xy$ such that this number is divisible by $80$, then $x+y=$?

Question 2 : If one-third of a two digit number exceeds its one-fourth by $8$, then what is the sum of the digits of the number?

Question 3 : If x, y are real numbers such that<br>$\displaystyle 3^{\displaystyle \frac{x}{y} + 1} - 3^{\displaystyle \frac{x}{y} - 1} = 24$, then the value of (x + y) / (x - y) is

Question 4 : The present age of a father is equal to the sum of the ages of &#160;his $5$ children. $12$ years hence, the sum of the ages of his children will be twice the age of their father. Find the present age of the father.

Question 5 : If $\displaystyle \frac{a}{3y}+\frac{3b}{x}=7$ and $\displaystyle a+1=2b+1=x=5,$ find the value of $'y'.$<br><br><br>

Question 6 : If $\sqrt[3]{5j - 7} = -\cfrac{1}{2}$, calculate the value of $j$.<br/>

Question 7 : 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?

Question 9 : If $\dfrac {2}{3x + 12} = \dfrac {2}{3}$, then the value of $x + 4 $ is

Question 10 : If $2^{x} + 2^{x&#160;+&#160;2} = 40$, then the value of $x$ is

Question 12 : Find the Solution&#160; : $x - cy - bz = 0 $&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160;$ cx - y +az = 0 $&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160;$bx+ ay -z = 0 $

Question 13 : A town's population had increased by $1200$ persons, and then its new population decreased by $11\%$. The town now has $32$ less persons than it did before the $1200$ increase. What was the original population?

Question 15 : The father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age. The present ages, in years, of the son and the father are, respectively.<br/>

Question 16 : If $\displaystyle \frac{x^2\, -\, (x\, +\, 1)(x\, +\, 2)}{5x\, +\, 1}\, =\, 6$, then $x$ is equal to

Question 17 : Present age of grandfather is ten times that of his granddaughter. He is also $54$ years older than her. Find their present ages.

Question 18 : Four times a certain two digit number is seven times the number obtained on interchanging its digits. If the difference between the digit is $4$, find the number.

Question 19 : It costs Rs. $10$ a kilometer to fly and Rs. $2$ a kilometer to drive. If one travels $200$ km covering $x$ km of the distance by flying and the rest by driving, then the cost of the trip is<br/>

Question 20 : The ages of Vivek and Sumit are in the ratio of $2 : 3$. After $12$ years, their ages will be in the ratio of $11 : 15$. The age of&#160;Sumit is

Question 22 : If &#160;$\sqrt{x+16} = x-4$, then the value of extraneous solution of the above equation is:

Question 25 : A combination of locks requires 3 numbers to open. The second number is $\displaystyle 2d + 5$ greater than the first number. The third number is $\displaystyle 3d - 20$ less than the second number. The sum of the three numbers is $\displaystyle 10d + 9$. The first number is

Question 26 : If&#160;$\displaystyle \sqrt{\left ( x-1 \right )\left ( y+2 \right )}=7$, $x$ and $y$ being positive whole numbers, then the values of $x$ and $y$ are, respectively

Question 27 : I have a total of Rs. $300$ in coins of denomination Re. $1$, Rs. $2$ and Rs. $5$. The number of Rs. $2$ coins is $3$ times the number of Rs. $5$ coins. The total number of coins is $160$. How many coins of each denomination are with me?

Question 28 : The ratio of boys to girls in a school is $5:2$. The number of boys is more by $450$ than that of girls. How many students are there in that school?<br>

Question 29 : A bus starts from city X. The number of women in the bus is half of the number of men. In city Y, $10$ men leave the bus and five women enter. Now, number of men and women is equal. How many passengers entered the bus in the beginning?

Question 30 : If you multiply a number by $3$ and then add $40$, the result is the same as if you first add $17$ and then multiply by $2$. What is the result if you subtract $9$ from the number and then multiply by $4$?

Question 32 : Let $a, b$ and $c$ be non-zero numbers such that $c$ is $24$ greater than $b$ and $b$ is $24$ greater than $a$. If $\dfrac {c}{a}&#160;= 3$, then find the value of $b$.

Question 33 : The solution of $3^{3x - 5} = \dfrac {1}{9^{x}}$ is __________.

Question 34 : When an iron rod is cut into equal pieces of $30$ cm each, a piece of $4$ cm is left out. When cut into equal pieces of $29$ cm, a piece of $13$ cm is left out. The minimum length of rod is

Question 36 : Find&#160;the value of $\dfrac {4}{y} + 4$ given that&#160;$\dfrac {4}{y} + 4 = \dfrac {20}{y} + 20$

Question 37 : Meera bought packs of trading cards that contain $10$ cards each. She gave away $7$ cards.<br>$x=$ Number of packs oftrading cards<br>Which expression shows the number of cards left with Meera?

Question 38 : A man covers a distance of $25$ km in an hour, partly on foot at the rate of $4$ km/hr and partly on motorcycle at $32$ km/hr. Find the distance travelled on the motorcycle.

Question 39 : The age of a man is $3$ times that of his son. $15$ years ago, the man was $9$ times as old as his son. What will be the age of man after $15$ years?

Question 40 : Instead of multiplying a given number by $\dfrac {8}{19}$, a student divided it by $\dfrac {8}{19}$. His answer was $297$ more than the correct answer. The given number is

Question 41 : A positive number is $5$ times another number. If $21$ is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?

Question 43 : Solve the linear equation: $5x - 12 = 2x + 18$<br/>

Question 44 : Ten years ago a father was six times as old as his daughter. After $10$ years, he will be twice as old as his daughter. Determine their present age.

Question 45 : A steamer going downstream in a river, covers the distance between $2$ towns in $15$ hours. Coming back upstream, it covers this distance in $20$ hours. The speed of the water is $3$ km/hr. Find the distance between two towns.

Question 46 : A thief is running at a speed of $6$ km per hour and a police constable is chasing him with a speed of $8$ km per hour. If originally, the distance between the thief and the constable is $500$ m. After what distance, will the constable catch the thief ?

Question 47 : A brand new car costs $ \$35,000$. For the first $50,000$ miles, it will depreciate approximately $\$0.15$ per mile driven. For every mile after that, it will depreciate by $\$0.10$ per mile driven until the car reaches its scrap value. Find the net worth of the car after it is driven $92,000$ miles.

Question 48 : Reduce the following linear equation: $6t - 1 = t - 11$<br/>

Question 49 : Find the value of $x: \dfrac {1}{x} + \dfrac {4}{5x} = \dfrac {2}{x + 5}$

Question 51 : What is the solution of $\displaystyle \frac{x-5}{2} - \frac{x-3}{5} = \frac{1}{2}$?

Question 52 : The sum of the digits of a two-digit number is $15$. If the number formed by reversing the digits is less than the original number by $27$, find the original number.

Question 54 : If Leah is $6$ years older than Sue and John is $5$ years older than Leah and the total of their ages is $41$. Then how old is Sue?

Question 55 : The number of solutions (x, y, z) to the system of equations $x+2y+4z=9, 4yz+2xz+xy=13, xyz=13$ such that at least two of x, y, z are integers is

Question 56 : The sum of three numbers is $855$. One of the numbers, $x$, is $50$% more than the sum of the other two numbers. What is the value of $x$ ?

Question 57 : The values of a so that the equation $\Vert x - 2\vert - 1\vert = a \vert x \vert$ does not contain any solution lying in the interval {2, 3} are

Question 58 : $Rs.\,3900.00$ has been distributed among the students (girls/boys) in a class in such a way that the girl student should get $Rs.\,80.00$ and boy should get $Rs.\,30.00$. The number of girl students in the class will be

Question 59 : $R = \dfrac{F}{N+F}$<br/>A website uses the formula above to calculate a sellers rating, $R$, based on the number of favorable reviews $F$, and unfavorable reviews $N$. Which of&#160;the following expresses the number of favorable&#160;reviews in terms of the other variables?<br/>

Question 61 : The number of solution of $ \left| \left[ x \right] -2x \right| =4$, where $[x]$ denotes the greatest integer less than&#160;$x$ is<br/>

Question 62 : State true or false:The root of the equation $\dfrac{y}{2}+6 = y$ is $\dfrac{1}{\sqrt{2}}$.<br/>