Reducing Equations to Simpler Form

Q.

A two digit number becomes five sixth of itself when its digits are reversed the two digit differ by 1 find the number

Q. Question 13
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 year) of the son and the father are respectively
(A) 4 and 24
(B) 5 and 30
(C) 6 and 36
(D) 3 and 24

Q.

Aman's age is three times his son's age. Ten years ago he was five times his son's age. Find their present ages.

Q.

Solve:

$\frac{7y+4}{y+2}=\frac{-4}{3}$

Q.

Three prizes are to be distributed in a quiz contest. The value of the second prize is $\frac{5}{6}$ of the value of the first prize and the value of the third prize is $\frac{4}{5}$ of the second prize. If the total value of the three prizes is Rs.1500. Find the value of each prize. (in order of 1^st, 2^nd & 3^rd)

1. Rs.500, Rs. 400, Rs.600

2. Rs. 600, Rs.500, Rs. 400

3. Rs.900, Rs.400, Rs.300

4. Rs.700, Rs.500, Rs.300

Q.

Solve the equation:$\frac{15}{4}-7x=9$

Q.

Solve the equation $\frac{0.4z-3}{1.5z+9}$ = $\frac{-7}{5}$

Q. Rene ages is 6 years older than her younger sister. After 10 years the sum their ages will be 50 years. Find their present ages .

Q.

Two years ago, Dilip was three times as old as his son and two years hence, twice his age will be equal to five times that of his son. Then the present age of Dilip is what?

Q.

Solve $\frac{3x-4}{7}+\frac{7}{3x-4}=\frac{5}{2}$

Q.

Find a two digit number which is three times the sum of its digits.

Q.

Mona's father is thrice as old as Mona. After 12 years he will be just twice his daughter. Their present ages are

1. 18 years, 36 years

2. 12 years, 36 years

3. 10 years, 30 years

4. 12 years, 24 years

Q.

The sum of the digit of a two digit number is 15 if the number formed by reversing the digit is less than the original number by 27 find the original number

Q.

If $f\left(x\right)=mx+c$ and if $f\left(0\right)=f\left(0\right)=1$ then $f\left(2\right)=$

1. $1$

2. $2$

3. $3$

4. $-3$

Q.

Ten years ago a father was four times as old as his son .After 20 years he will be twice as old as his son .Determine the present age of the son.

Q.

Question 105

Solve the following:

An employee works in a company on a contract of 30 days on the condition that he will receive Rs. 120 for each day he works and he will be fined Rs. 10 for each day he is absent. If he receieves Rs. 2300 in all, for how many days did he remain absent?

Q.

A car travels 165 km in 3 hours.

How long will it take to travel 440 km?

Q. Twenty years ago, my age was 1/3 of what it is now. What is my age

Q.

If $y$ be an implicit function of $x$ defined by $x^{2x}-2x^x\cot \left(y\right)-1=0$, then $y\left(1\right)$ is equal to

1. $-1$

2. $1$

3. $\log \left(2\right)$

4. $-\log \left(2\right)$

Q.

A class has the same number of girls and boys. Only eight boys were absent on a particular day and then the number of girls was double the number of girls. What is the number of boys and girls?

Q.

Write an equation for which $0$ is a solution.

Q.

sheela is now 15 years older than her yonger brother Sanjay ten years from now sheela will be twice as old as sanjay find the present age of each

Q. If the sum of the age of A and B is 30 years. Just after the five years A age will be three time older than B . Find thier present age.

Q.

Three prizes are to be distributed in a quiz contest. Total prize is Rs.1000. Second prize will be given $\frac{3}{4}$ of the first prize and third prize will be given $\frac{1}{3}$ of the second prize. Find the money given to each contest. [4 MARKS]

Q. Five years ago, Rahul’s father was $5$ times as old as Rahul. But $5$ years from now, Rahul’s father will be $3$ times as old as his son. The present age of Rahul is

1. $12$ years
2. $10$ years
3. $15$ years
4. $18$ years

Q.

Sum of digit 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. check your solution.

Q.

Cost of 20 Pencils is 100 Rupees. Cost of a pen is 40 more than 8 times the cost of a Pencil. Find the cost of 5 Pencils and 6 Pens.

1. 405 Rupees

2. 505 Rupees

3. 300 Rupees

4. 200 Rupees

Q.

Solve : $\frac{4-3x}{5}+\frac{7-x}{3}+4\frac{1}{3}=0$ Hence find the value of 'p' if $3p-2x+1=0$

Q.

If $\omega =\frac{z}{z-\left({\displaystyle \frac{1}{3}}\right)i}$ and $\left|\omega \right|=1$, then $z$ lies on

1. A parabola

2. A straight line

3. A circle

4. An ellipse

Q.

A student gets 3 marks for answering a question correctly and loses 1 mark for answering it wrong. Suppose, he answers 5 correct questions and 2 wrong questions, then the total marks scored by him is

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