Simple or linear Equations: Tricks and Examples. I have already discussed a concept - Quadratic Equations of quantitative aptitude. Today I will discu

Examples with solutions

Example1: If $3x+6=4x-2$, then find the value of x?
1. 8 2. 4 3. 6 4. 7
Solution: $3x+6=4x-24x-3x=6+2x=8$ Using a trick: By removing the possibilities, this question is simple to resolve.
Firstly check option(1) whether it satisfies the equation or not
$3(8)+6=4(8)-230=30$ 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: The basic strategy for answering this question is the same as for the previous one; simply enter the provided values into the equation and determine which ones satisfy it.  Start with the first option i.e. 2,1
Put x $=2$ and $y=1$ in both equations and check if both equations satisfies. $2x+y=52(2)+1=55=5$
$3x-2y=43(2)-2(1)=44=4$ 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 $\Rightarrow 39$ 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, $x+x+2+x+4=30\Rightarrow 3x=24\Rightarrow x=8$ 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
$1P+2B=703P+9B=300$
Eliminating the options, only second option will satisfy the equations,
$1P+2B=70\Rightarrow 1(10)+2(30)=70\Rightarrow 70=70$
$3P+9B=300\Rightarrow 3(10)+9(30)=300\Rightarrow 300=300$
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.