### Simplification With Important Concepts And New Pattern Questions

We all know that simplification is most important topic asked in every competitive exam like banking and ssc. So lets try to understand what is actually meant of ‘simplification’.
Simplification is most easy and important topic for banking, SSC and other govt. exam perspective. Simplification is based on basic mathematics calculations and some other algebra topics. It is less time consuming and having higher accuracy.
Simplification questions are asked in the exam to check the ability of students deal with the numbers. Two important types:
1). Sometimes, a calculation is given and one of the numbers is missing from the calculation and to find the missing numbers.
2). Sometimes all the numbers are given with some operations between the numbers and we have to simplify the calculation.
Some topics on which simplification is based on like:
(i) BODMAS rules.
(ii) Percentages.
(iii) Squares.
(iv) Cubes.
(v) Approximations.
Tricks and techniques on how to solve the question:

### BODMAS rules

this rule always keep in the mind it’s very important and helpful in solving the questions. Whenever we have more than one operation in the given question of simplification, we have to do the operations according to the priority by BODMAS.
B – Stands for bracket and operation of brackets in the order ( ), { } and [ ]
O – ‘of’(usage as multiplication *) [but its apply in the questions before multiplication]
D – Division (/)
M – Multiplication (*)
S – Subtraction (-)
In the simplification questions some calculation solve by the algebra formula, some formulas given below:

### Problems

(1). 124% of 3250 + (3/8) of 5712 = (?)2 + 243
Solution:
(124/100) * 3250 + (3/8) * 5712 = x2 + 243
4030 + 2142 –243 = x2
x2 = 5929
x = 77

(2). ? % of 600 = 3285 – (442 – 192) * 19 ÷ 399
Solution:
(x/100) * 600 = 3285 – [(44 + 19) (44 – 19) * 19 ÷ 399]
[ here apply the algebra formula a2 – b2]
6x = 3285 –[63 * 25 * 19/399]
6x = 3285 –75
6x = 3210
x = (3210/6) = 535

(3). 72 * 6 * (125 – 97) + 1254 ÷ 3 ÷ 11 – 662 = ?
Solution:
(72 * 6 * 28) + 1254 ÷ 3 ÷ 11 – 662 = x
12096 + 38 – 4356 = x
x = 7778

(4). (5/17) of (408/55) of (165/240) of 6000 = 25 % of ?
Solution:
(5/17) * (408/55) * (165/240) * 6000 = (25/100) * x
x = 36000

(5). (422 – 182) x 24 ÷ 128 + ? % of 1800 = 1080
Solution:
(42 + 18) (42 –18) × 24 ÷ 128 + (x/100) * 1800 = 1080
[ here apply the algebra formula a2 – b2]
[60 * 24 * 24/128] + 18x = 1080
(34560/128) + 18x = 1080
270 + 18x = 1080
18x = 1080 –270
18x = 810
x = (810/18) = 45

(6). (7 × 7)4 ÷ (343 ÷ 7)2 × (343 × 7)3 = (7)? + 5
Solution:
78 ÷ (49)2 × (73 × 7)3 = (7)x + 5
78 ÷ 74 × 712 = (7)x + 5
78 – 4 + 12 = 7x + 5
716 = 7x + 5
16 = x + 5
x = 11

(7). 114 % of 1250 + (4/7) of 5712 = (?)2 + 65
Solution:
(114/100) * 1250 + (4/7) * 5712 = x2 + 65
1425 + 3264 – 65 = x2
x2 = 4624
x = 68

(8). (3/7) of 245 × 135 ÷ 15 – ? = 528 ÷ 3 + 217
Solution:
(3/7)*245*(135/15) – x = (528/3)+217
945-x = 176+217
x = 945 – 176 – 217
x = 552

(9). 465 × 7 + 12.5 % of 658 + 876.75 =?
Solution:
465 * 7 + 12.5% of 658 + 876.75 = x
3255 + 82.25 + 876.75 = x
4214 = x

(10). (550 % of 250) ÷ 275 + 45 % of 780 =?
Solution:
(550% of 250) ÷ 275 + 45% of 780 = x
1375 ÷ 275 + 351 = x
5 + 351= x
356 = x

(11). 378.35 + 478 ÷ 12.5 + 456.41 =?
Solution:
378.35 + 478 ÷ 12.5 + 456.41 = x
378.35 + 38.24 + 456.41 = x
873 = x

(12). 37.5% of 80% of 730 + 160% of 250 – ? = 120% of 400
Solution:
37.5% of 80% of 730 + 160% of 250 – x = 120%of400
219 + 400 – x = 480
139 = x

(13). 87×26÷82.4×81.4 = 8?
Solution:
87 × 26 ÷ 82.4 × 81.4 = 8x
87 * 82 ÷ 82.4 * 81.4 = 8x
87 + 2 – 2.4 + 1.4 = 8x
88 = 8x
x = 8

(14). ? %of(75×4–150) = 420+752
Solution:
X % of (75 × 4 – 150) = 420 + 752
(x/100)*(300 – 150) = 420 + 5625
(x/100)*150 = 6045
3x/2 = 6045
x = 6045*(2/3) = 4030

(15). 34 % of 4200 – 510 ÷? + 72 % of 400 = 1713
Solution:
34 % of 4200 – 510 ÷ x + 72 % of 400 = 1713
(34/100)*4200 – (510/x) + (72/100)*400 = 1713
1428 + 288 – 1713 = (510/x)
3 = (510/x)
x = 510/3 = 170

(16). 11 5/8 + 4 7/16 – 9 3/8 + 12 3/16 = ? – 3 7/8
Solution:
11 5/8 + 4 7/16 – 9 3/8 + 12 3/16 + 3 7/8 = x
x = (11 + 4 – 9 + 12 + 3) (5/8 + 7/16 – 3/8 + 3/16
+ 7/8)
x = 21 28/16 = 21 7/4 = 22 ¾

(17). (8 × 8)5 ÷ (512 ÷ 8)2 × (8 × 64)3 = (8)? + 5
Solution:
(82)5 ÷ (512/8)2 × (8 × 82)3 = (8)x + 5
810 ÷ (64)2 × (83)3 = (8)x + 5
810 ÷ 84 × 89 = (8)x + 5
810 – 4 + 9 = 8x + 5
815 = 8x + 5
15 = x + 5
x = 10

(18). ? % of (28 × 9 – 72) = 350 + 352
Solution:
x % of (28 × 9 – 72) = 350 + 352
(x/100) * [252 – 72] = 350 + 1225
(x/100) * 180 = 1575
x = (1575 * 100)/180 = 875
x = 875

(19). 164.5 × 46.3 × 82.1÷ 29.2 × 320.64 = 82.3 + ?
Solution:
164.5 × 46.3× 82.1 ÷ 29.2 × 320.64 = 82.3+ ?
24 × 4.5 × 22 × 6.3 × 23 × 2.1 ÷ 29.2 × 25 × 0.64 = 2[3 × 2.3 + 3 ?]
218 × 212.6 × 26.3 ÷ 29.2 × 23.2= 2(6.9 + 3 ?)
2(18 + 12.6 + 6.3 – 9.2 + 3.2)= 2(6.9 + 3 ?)
18 + 12.6 + 6.3 – 9.2 + 3.2 = 6.9 + 3?
30.9 = 6.9 + 3?
24 = 3?
? = 8

(20). (47 + 47 + 47 + 47 + 47 + 47) × 5 × (47 + 47) × 6 ÷ (47 × 2) = 47 × ?
Solution:
(47 + 47 + 47 + 47 + 47 + 47) × 5 × (47 + 47) × 6 ÷ (47 × 2) = 47 × ?
47 × 6 × 5 × 47 × 2 × (6/47×2)= 47 × ?
47 × 6 × 5 × 6 = 47 × ?
? = 180

(21). ? % of 699 – 24 % of 1548 –(11/17) of (35/18) of 71 = 30
Solution:
? % of 699 –24 % of 1548 – (11/17) of (35/18) of 71 = 30
(x/100) * 700 –(24/100) * 1550 -(11/17) * (34/18) * 72 = 30
7x –372 –88 = 30
7x = 490
x = 70

### What approximate value should come in the place of question mark (?) in the following questions ?

(1). ? = (4128 + 574) ÷ 25 + (18.23)2+ (2/15) of 12524 –24
Solution:
? = (4128 + 574) ÷ 25 + (18.23)2+ (2/15) of 12524 –24
x = (4128 + 574)/25 + 182+ (2/15) * 12525 –24
x = (4702/25) + 324 + 1670 –24
x = 188 + 324 + 1670 –24
x = 2158 = 2160 approx.

(2). 34478 ÷ 8 + (3/13) of 12154 + 30 % of 599 = ?2–274
Solution:
34478 ÷ 8 + (3/13) of 12154 + 30 % of 599 = ?2–274
(34480/8) + (3/13) * 12155 + (30/100)*600 = x2–274
4310 + 2805 + 180 + 274 = x2
7569 = x2
x = 87 approx.

(3). (3.2/7) of 348 + (5/7) of (21.2/14.8) of 1897 = ? % of 499
Solution:
(3.2/7) of 348 + (5/7) of (21.2/14.8) of 1897 = ? % of 499
(3/7) of 350 + (5/7) of (21/15) of 1900 = x % of 500
(3/7) * 350 + (5/7) * (21/15) * 1900 = (x/100) * 500
150+ 1900 = 5x
2050 = 5x
x = 2050/5 = 410 approx.

(4). 17 % of ? –2054 ÷ 12.78 -222 ÷ 3.01 = 57
Solution:
17 % of ? –2054 ÷ 12.78 -222 ÷ 3.01 = 57
(17/100) * x –(2054/13) -(222/3) = 57
(17/100) * x = 57 + 158 + 74
(17/100) * x = 289
x = 1700 approx.

(5). (4.3 / 6.78) of 48.7 × 15 ÷ 5.12 + ? = 129.68
Solution:
(4.3 / 6.78) of 48.7 × 15 ÷ 5.12 + ? = 129.68
(4 / 7) * 49 × (15 / 5) + x = 130
84 + x = 130
x = 130 –84 = 46

(6). (1782 ÷ 11.98) ÷ 2.92 × 35.89 + 25 % of 541 –67 % of 1299 = ?
Solution:
(1782 ÷ 11.98) ÷ 2.92 × 35.89 + 25 % of 541 –67 % of 1299 = ?
(1782/12) × (1/3) × 36 + (25/100) × 540 –(67/100) × 1300 = x
1782 + 135 –871 = x
x = 1046

(7). (63.89)2× (64.12)1/3× (25.99)2÷ (211× (12.77)2) = 2x
Solution:
(63.89)2×(64.12)1/3× (25.99)2÷ (211× (12.77)2) = 2x
(64 × 64 × 4 × 26 × 26) / (211× 13 × 13) = 2x
(26× 26 × 24)/ 211= 2x
26 + 6 + 4 -11= 2x
25= 2x
x = 5

(8). 35 % of 1593 + 29 % of 4506 = ? × 41 + 468 + 773.89 –199.78
Solution:
35 % of 1593 + 29 % of 4506 = ? × 41 + 468 + 773.89 –199.78
(35/100) * 1600 + (29/100) * 4500 = 41x + 468 + 774 -200
560 + 1305 -468 –774 + 200 = 41x
823 = 41x
x = 820/41 = 20

(9). (1023.77)2 ÷ (255.89)3/2 × 64.12 = (3.92)4× 4?
Solution:
(1023.77)2 ÷ (255.89)3/2 × 64.12 = (3.92)4× 4?
(1024)2 ÷ (256)3/2 × 64 = 44× 4x
(45)2÷ (44)3/2× 43= 44× 4x
410÷ 46× 43= 44× 4x
410–6 + 3 –4= 4x
43= 4x
x = 3

(10). 19.99 % of 25501 + √9410 × 2.904 -√4760 = ?
Solution:
19.99 % of 25501 + √9410 × 2.904 -√4760 = x
20 % of 25500 + √9409 × 3 -√4761 = x
(20/100) * 25500 + 97 * 3 –69 = x
5100 + 291 -69 = x
5322 = x

(11). 45.098 × 5.998 + 72.002 ÷ 7.990 + 2.999 × 6.999=?
Solution:
45.098 × 5.998 + 72.002 ÷ 7.990 + 2.999 × 6.999 = x
45 * 6 + 72/ 8 + 3 * 7 = x
270 + 9 + 21= x
300 = x approx.