Friday, February 28, 2014

Simple or linear Equations: Tricks and Examples.

Posted by Jasleen Behl
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.

Examples with solutions

Example1: If `3x + 6` = `4x - 2`, then find the value of `x`?
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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