I have already discussed a concept - Quadratic Equations of quantitative aptitude. Today I will discuss some examples of simple equations which have been proved to be a very important topic for various competitive exams. The problems of linear equations can be easily solved by using simple tricks. Lets discuss how.

According to ques,

## Examples with solutions

**1.**8

**2.**4

**3.**6

**4.**7

**Solution:**`3x + 6 = 4x-2`

`4x - 3x` = `6 + 2`

x = `8`

By using trick: This question can be easily solved by eliminating the options.

Firstly check option(1) whether it satisfies the equation or not

`3(8) + 6 = 4(8) - 2`

`30 = 30`

Therefore,`8` satisfies the equation.

Hence the answer is x = `8`

**Example2:**If `2x + y` = 5 and `3x - 2y` = 4, then find the value of x and y.

**1.**`2,1`

**2.**`3,-1`

**3.**`4,4`

**4.**`2,-2`

**Solution:**Basic trick for this question is same as previous, just put the given values in equation and check which one is satisfying the equation.

Start with the first option i.e. `2,1`

Put `x = 2` and `y = 1` in both equations and check if both equations satisfies.

`2x + y = 5`

`2(2) + 1 = 5`

`5=5`

`3x - 2y = 4`

`3(2) - 2(1) = 4`

`4=4`

Therefore, first option is satisfying the equation.

**Example3:**The sum of digits of two digit number is 12. If 54 is subtracted from the number, the digits gets reversed. Find the number.

**1.**`39`

**2.**`85`

**3.**`93`

**4.**`75`

**Solution:**In above question two statements are given i.e

**Sum of digits of two digit number is 12**and

**If 54 is subtracted from the number, the digits gets reversed.**

All the options except `85` satisfies the first statement. Therefore, reject the second option.

Now we are left with `1,3` and `4`.

If 54 is subtracted from the number ⇒ `39` is rejected as `54 > 39`, we cannot subtract bigger number.

So, we are left with only `93` and `75`.

According to second statement,

`93 - 54 = 39` Digit reversed

Therefore, answer is 93.

**Example4:**The sum of three consecutive even numbers is 30. Find the difference of the squares of extreme numbers.

**Solution:**Three consecutive even numbers = `x , x+2 , x+4`

According to ques,

`x + x +2 + x + 4` = `30`

⇒ `3x = 24`

⇒ `x = 8`

Therefore, numbers are 8, 10 and 12.

Difference of squares of extreme numbers = `(12)^2 - 8^2 = 144 - 64 = 80`

**Example5:**The cost of one pen and two books together is Rs.70. The cost of 3 pens and 9 books is Rs.300. Find cost of book and pen.

**1.**20, 15

**2.**30, 10

**3.**40, 5

**4.**25, 6

**Solution:**Let cost of one pen is P and cost of one book is B

1P + 2B = 70

3P + 9B = 300

Eliminating the options, only second option will satisfy the equations,

`1P + 2B = 70`

⇒`1(10) + 2(30) = 70`

⇒`70=70`

`3P + 9B = 300`

⇒`3(10) +9(30) = 300`

⇒`300 =300`

**Example6:**p, q, r, s, t are five consecutive numbers in increasing order. If r + s + t + p =101, then find product of q and r.

**Solution:**Try to solve it yourself. Answer: 600

In this way, you can easily solve simple or linear equations problems. It helps you save your time in exam.

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