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 (*)

**A** – Addition (+)

**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 = x^{2} + 243

4030 + 2142 –243 = x^{2}

x^{2} = 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 = x

^{2}+ 65

1425 + 3264 – 65 = x2

x

^{2}= 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.