Quantitative Aptitude – Simplification
Simplification is the process of finding the most simplest form of a given expression. In competitive exam simplification is another important topic. At least two or three questions are from simplification. So, now we will discuss the details of simplification here in this page.
An equation may consist few numbers and few arithmetic operators in it. And, we can simplify the equation on the basis of priority of the operators. So, we need to know which operators has most priority and which has less. And, here comes a rule known as BODMAS rule.
As we know that BODMAS rule tells us about the priority of the operators. So, what does BODMAS stands for-
- B = Bracket
- O = Of
- D = Division
- M = Multiplication
- A = Addition
- S = Subtraction
This means, first of all we need to remove brackets from the expression, if any. Brackets should be removed in order of, (), {} and then []. Then we do “Of” operations and so on in the following order.
And, one more important thing is Virnaculum or Bar. If an expression has virnaculam then apply the virnaculam first on the expression. BODMAS rule will be applied on the expression after virnaculam.
Few examples of Simplification
Simplification: Example 1
Simplification of: 16200 / 270 / 30
Answer: If your answer is 1800 then you are wrong. If your answer is 2 then your are right. And, do division from left to right. So, first of all (16200 / 270) = 60. Then divide 60 with 30 and the result will be 2.
Simplification: Example 2
Simplification of: 2540 + (340 / 17)
Answer: According to BODMAS rule, first of all we need to simplify the expression which are within brackets. So, 340 / 17 = 20. Now, add this result with the remaining portion of the expression. 2540 + 20 = 2560 will be the answer.
Simplification: Example 3
A man has some hens and cows. Now, total number of heads be 100 and total number of feet equals 316. So, find the number of hens and cows that man have.
Answer: Let the number of hens be x and the number of cows be y.
x + y = 100 …….. (i)
As hens has two legs and cows has four legs, so, 2x + 4y = 316 or x + 2y = 158 …….. (ii)
Solving (i) and (ii) we get:
x + 2y = 158
x + y = 100
(-)
———————-
y = 58
So, x = (100 – y) = 42
Therefore, the number of hens be 42 and number of cows be 58.
Few Examples to Test your Simplification learnings:
Example #1
25% of 1400 + 12% of 5250 = ?
25% of 1400 + 12% of 5250 = ?
So, in this example we need to simplify the expression and find the value. And, to do this we need to follow the BODMAS rule.
So, here we see Addition and Percentage of a value. And, according to BODMAS rule we do percentage calculation first then addition.
Like,
25% of 1400 + 12% of 5250 = ?
so, ? = (25 / 100) x 1400 + (12 / 100) x 5250 Simplified expression
or, ? = 350 + (12 / 100) x 5250
or, ? = 350 + 630
finally, ? = 980
Example #2
15000 / 40 / 25 / 5
15000 / 40 / 25 / 5
So, in this example we need to find the simplified value of the expression. And, to do this we need to follow the BODMAS rule.
So, here we see only Division. And, according to BODMAS rule we simplify this expression from left to right.
Like,
15000 / 40 / 25 / 5
or, 375 / 25 / 5
or, 15 / 5
finally, 3
Example #3
As we all know that Snakes does not have legs.
So, all legs counts are Spider's legs.
Therefore, we can say that, all 784 legs are Spider's leg.
One spider has 8 legs.
So, total number of spider in that group is:
784 / 8
= 98
Therefore, the total number of Snakes are,
125 - 98
= 27
Example #4
Let, the number of Bulls in the farm is Y.
So, the number of Cows in the farm is 10Y.
Total animals present in the farm is,
10Y + Y
= 11Y
So, the answer must be a multiple of 11.
And, the only option here, which is multiple of 11 is, 44.
Example #5
Working hours for 6 weeks is,
6 days x 8 hours x 6 weeks
= 6 x 8 x 6
= 288 hours.
Suppose, the computer operator works overtime for X hours.
Therefore,
(288 x 50) + (75X) = 16275
75X = 16275 - 14400
75X = 1875
X = 25
So, the computer operator works for,
288 + 25
= 313 hours.
Example #6
Let, the number of Green balls in the bucket is Y.
So, the number of Red balls in the bucket is 5Y.
Total balls present in the bucket is,
5Y + Y
= 6Y
So, the answer must be a multiple of 6.
And, the only option here, which is multiple of 6 is, 54.
Example #7
Let, the share of C is X.
Therefore, the share of B is: X/2.
And, the share of A is: 1/4 x X/2 = X/8
Therefore,
X/8 + X/2 + X = 130
(X + 4X + 8X) / 8 = 130
13X/8 = 130
X = (130 x 8) / 13
X = 10 x 8
So, X = 80
Hence, B's share is:
X/2
= 80 / 2
= 40
Example #8
As mentioned in the question that 2501 steps is needed to cover the whole distance. And, the gap between each step is also equal.
So, we can say that 2501 steps has 2500 equal distance between them. And, this is also the total distance from his home to the shop, i.e, 2.5 kilometer or 2500 meters.
So, the gap between two consecutive step is:
2500 / 2500
= 1.0 meters.
Example #9
35% of 560 + ?% of 780 = 469
35% of 560 + ?% of 780 = 469
So, in this example we need to simplify the expression and find the missing value. And, to do this we need to follow the BODMAS rule.
So, here we see Addition and Percentage of a value. And, according to BODMAS rule we do percentage calculation first then addition.
Like,
Let, the missing number be A. So,
35% of 560 + A% of 780 = 469
(35 / 100) x 560 + (A / 100) x 780 = 469 Simplified expression
196 + (A / 100) x 780 = 469
196 + (780A / 100) = 469
19600 + 780A = 46900
780A = 46900 - 19600
780A = 27300
A = 27300 / 780
A = 35
Example #10
10 + [-18 + 2 {-52 / 4 + 55 - 21}]
10 + [-18 + 2 {-52 / 4 + 55 - 21}]
So, in this example we need to find the simplified value of the expression. And, to do this we need to follow the BODMAS rule.
So, here we see Bracket, Addition, Subtraction, Multiplication and Division. And, according to BODMAS rule we do brackets first then division then multiplication then addition and then subtraction.
Like,
10 + [-18 + 2 {-52 / 4 + 55 - 21}]
or, 10 + [-18 + 2 {-13 + 55 - 21}]
or, 10 + [-18 + 2 {42 - 21}]
and, 10 + [-18 + 2 x 21]
or, 10 + [-18 + 42]
or, 10 + 24
finally, 34
So, if you need any farther help on Simplification, then let us know. And, We will discuss on those problems here in www.AptitudeTricks.com. Feel free to ask your questions.