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*. This is one of the easiest and most important topics for Numerical Ability section of Clerical level exams. People tend to confuse for these type of problems. But trust me, these type of problems are very easy. Just follow the methods shown below. You can solve them in fraction of seconds. All the Best :)*

**Problems on Numbers**## Problems on Numbers Shortcuts

**:**

__Model 1__**If two-third of one-fifth of three-seventh of a number is 4, what is the number ?**- 60
- 70
- 75
- 80
- None of these

**Solution**:

Given that two third (2/3) of one fifth (1/5) of three seventh (3/7) of a number is 4.

Say that number is

*x*, So
(2/3)×(1/5)×(3/7)

*x*= 4
=>

*x*= 70

__Practice Problems on Model 1__:**If three-fourth of four-ninth of three-fifth of a number is 16, what is the number ?**- 60
- 70
- 75
- 80
- None of these
**If three-seventh of seven-ninth of three-fourth of a number is 15, what is the number ?**- 60
- 70
- 75
- 80
- None of these
**If two-ninth of nine-fourteenth of 2 1/3 times of a number is 25, what is the number ?**

__Model 2__:**If three-fifth of two-seventh of a number is 24, what is its 40% ?**- 56
- 64
- 120
- 140
- None of these

**Solution :**

Say the number is

*n*
(3/5)

*× (2/7) ×**n*= 24
=>

*n*= 140**Caution Note**: As soon as we see the number 140, hurriedly we mark option 4 as the answer. But here in the question, they didn't ask us the number. They asked 40% of the number. So we need to find the percentage.

So the answer will be 140 × (40/100) = 56

__Practice Problems on Model 2__:**If four-fifth of five sixth of a number is 120, what is its 66 2/3 % ?**- 56
- 64
- 120
- 140
- None of these
**If three seventh of seven-fifteenth of a number is 84, what is its 33 1/3 % ?**- 56
- 64
- 120
- 140
- None of these
**If eighteen-nineteenth of 4 3/4 times of a number is 128, what is its 225% ?**- 56
- 64
- 120
- 140
- None of these

**:**

__Model 3__**If three-fourth of two-third of a number is 12, what is the sum of its digits ?**- 12
- 8
- 7
- 5
- None of these

**Solution :**

(3/4) × (2/3) ×

*n*= 12*n*= 24

Sum of its digits is 2 + 4 = 6

__Practice Problems on Model 3__:**If three-fourth of two-third of 65% of a number is 156, what is the sum of its digits ?**- 12
- 8
- 7
- 5
- None of these
**If nine-thirteenth of five-sixth of 62.5% of a number is 225, what is the sum of its digits ?**- 12
- 8
- 7
- 5
- None of these
**If seven-twelfth of three-eighth of 84% of a number is 147, what is the sum of its digits ?**- 12
- 8
- 7
- 5
- None of these

**:**

__Model 4__**Two-third of the first number is same as three-fourth of the second number. What is their ratio ?**- 8:9
- 6:7
- 9:8
- 7:6
- None of these

**Solution :**

Say the first number is F and the second number is S

(2/3)×F = (3/4)×S

=> F/S = 9/8

__Practice Problems on Model 4__:**Three-fourth of the first number is same as 87.5% of the second number. What is their ratio ?**- 8:9
- 6:7
- 9:8
- 7:6
- None of these
**Three-fourth of the first number is same as two-third of the second number. What is their ratio ?**- 8:9
- 6:7
- 9:8
- 7:6
- None of these
**7 times of the first number is same as six times of the second number. What is their ratio ?**- 8 : 9
- 6 : 7
- 9 : 8
- 7 : 6
__None of these__

**:**

__Model 5__**Sum of a two digits number and the number obtained by interchanging the digits is 44. What is the sum of the digits of the number ?**- 4
- 5
- 6
- 7
- None of these

**Solution :**

If the two digits are

*x*and*y*,*x*is on 10s place and

*y*is on units place => 10

*x+y*

The number obtained by interchanging the digits is

*=>*10*y+x*
So,

10

*x+y*+ 10*y+x*= 44
=> 11

*x*+11*y*= 44
=>

*x+y*= 4__:__

**Practice Problems on Model 5****Sum of a two digits number and the number obtained by interchanging the digits is 77. What is the sum of the digits of the number ?**- 4
- 5
- 6
- 7
- None of these
**Sum of a two digits number and the number obtained by interchanging the digits is 55. What is the sum of the digits of the number ?**- 4
- 5
- 6
- 7
- None of these
**Sum of a two digits number and the number obtained by interchanging the digits is 66. What is the sum of the digits of the number ?**- 4
- 5
- 6
- 7
__None of these__

__Model 6__:**Difference between a two-digits number and the number obtained by interchanging the digits is 36. What is the difference between the digits of the number ?**- 4
- 5
- 6
- 7
- None of these

**Solution :**

Here, they asked the difference.

So,

(10

*x+y*) - (10*y+x*) = 36
10

*x+y*-10*y-x*= 36
=> 9

*x*- 9*y*= 36*x-y*= 4

__Practice Problems on Model 6__:**Difference between a two-digits number and the number obtained by interchanging the digits is 45. What is the difference between the digits of the number ?**- 4
- 5
- 6
- 7
- None of these
**Difference between a two-digits number and the number obtained by interchanging the digits is 54. What is the difference between the digits of the number ?**- 4
- 5
- 6
- 7
- None of these
**Difference between a two-digits number and the number obtained by interchanging the digits is 63. What is the difference between the digits of the number ?**- 4
- 5
- 6
- 7
- None of these

**:**

__Model 7__**Sum of a two-digits number and the number obtained by interchanging the digits is 55. Which one of the following could be the difference between the digits of the number ?**- 2
- 3
- 4
- 7
- 8

**Solution :**

Here, the Sum of a two-digits number and the number obtained by interchanging the digits is 55.

That means, the numbers should be,

32 23, 14 41, 23 32, 41 14

Difference between the digits of the numbers is

3-2 = 1,

4-1 = 3

3-2 = 1

4-1 = 3

From the given options, the answer is

**3**

__Practice Problems on Model 7__:**Sum of a two-digits number and the number obtained by interchanging the digits is 66. Which of the following could be the difference between the digits of the number ?**- 1
- 3
- 4
- 7
- 8
**Sum of a two-digit number and the number obtained by interchanging the digits is 88. Which of the following could be the difference between the digits of the number ?**- 1
- 3
- 5
- 7
- 8
**Sum of a two-digits number and the number obtained by interchanging the digits is 33. Which of the following could be the difference between the digits of the number ?**- 1
- 5
- 4
- 7
- 8

**Important Points to Note**:

- The
**sum**of a 2 digit number and the number obtained by interchanging the digits is always divisible by**11**. - The
**difference**between a two digit number and the number obtained by interchanging the digits of that number is always divisible by**9.** - If the
**sum**of a 2 digit number and the number obtained by interchanging the digits of that number is given, the**difference**of the digits cannot be exactly found. - If the
**difference**of a 2 digit number and the number obtained by interchanging the digits of that number is given, the**sum**of the digits cannot be exactly found.

__:__

**Model 8****Difference between a two-digits number and the number obtained by interchanging the digits is 54. Which of the following could not be the sum of the digits of the number ?**- 6
- 8
- 10
- 12
- 14

**Solution :**

56/9 = 6 [Difference of digits]

So the digits should be 9 3, 8 2, 7 1, 6 0

According to given options, 14 is NOT the sum of the digits of the number.

**:**

__Practice Problems on Model 8__**Difference between a two-digits number and the number obtained by interchanging the digits is 36. Which of the following could not be the sum of the digits of the number ?**- 6
- 8
- 9
- 12
- 14
**Difference between a two-digits number and the number obtained by interchanging the digits is 45. Which of the following could not be the sum of the digits of the number ?**- 3
- 5
- 7
- 9
- 11
**Difference between a two-digits number and the number obtained by interchanging the digits is 63. Which of the following could not be the sum of the digits of the number ?**- 7
- 9
- 11
- 13
- None of these

__:__

**Model 9****Sum of the digits of a two digits number is 9. When the digits are interchanged the number will be decreased by 9. What is the number ?**- 63
- 36
- 45
- 54
- None of these

**Solution :**

Sum of the digits of a two digits number = 9

=> x+y = 9 --------------> (1)

Given that, when the digits are interchanged, the number will be decreased by 9

that means (10x+y) - (10y-x) = 9

10x+y-10y-x = 9

9x - 9y = 9

=> x-y = 9 --------------> (2)

From (1) and (2)

x+y = 9

x-y = 1

_______

2x = 10

=> x = 5

so y = 4

So the number xy = 54

__:__

**Practice Problems on Model 9****Sum of the digits of a two digits number is 9. When the digits are interchanged the number will be decreased by 27. What is the number ?**- 63
- 36
- 45
- 54
- None of these
**Sum of the digits of a two digit number is 9. When the digits are interchanged the number will be increased by 9. What is the number ?**- 63
- 36
- 45
- 54
- None of these
**Sum of the digits of a two digits number is 9. When the digits are interchanged the number will be increased by 27. What is the number ?**- 63
- 36
- 45
- 54
- None of these

**:**

__Model 10__**When 45 is added to a number, it will be increased by 20%. What is the number ?**- 225
- 240
- 270
- 300
- None of these

**Solution**:

When 45 is added to a number, it will be increased by 20%

that means 20% -----> 45

So, multiply with 5 on both sides,

100% ----- 45x5 =

**225**
225 is the answer

**:**

__Practice problems on Model 10__**When 81 is added to a number, it will be increased by 30%. What is the number ?**- 225
- 240
- 270
- 300
- None of these
**When 96 is added to a number, it will be increased by 40%. What is the number ?**- 225
- 240
- 270
- 300
- None of these
**When 75 is added to a number, it will be increased by 25%. What is the number ?**- 225
- 240
- 270
- 300
- None of these

**Note**: In some cases you cant directly equate it to 100 by multiplying with any number. Then follow below method.

30% ------> 81

Here you can't get 100 by multiplying any number with 30

So, just equate it to the near double zero digit.

So, multiply with 10

=> 300% -----> 810

Now divide with 3

=> 100% ----> 270

__:__**Model 11****When 20 is subtracted from a number. It will be decreased by its 25%. What is the number ?**- 60
- 75
- 80
- 96
- None of these

**Solution**:
25% ------ > 20

100% ----------------> 80 (multiplied by 4)

**Practice Problems on Model 11**:**When 30 is subtracted from a number, it will be decreased by its 50%. What is the number ?**- 60
- 75
- 80
- 96
- None of these
**When 18.75 is subtracted from a number, it will be decreased by its 25%. What is the number ?**- 60
- 75
- 80
- 96
- None of these
**When 38.4 is subtracted from a number, it will be decreased by its 40%. What is the number ?**- 60
- 75
- 80
- 96
- None of these

__:__

**Model 12****When 30 is subtracted from a number, it will be decreased to its 80%. What is the number ?**- 120
- 150
- 180
- 225
- None of these

**Solution :**

When 30 is subtracted from a number, it will be decreased to its 80%, that means it will be reduced by 20%

=> 20% ----> 30

100% -----> 150

__:__

**Practice Problems on Model 12****When 18 is subtracted from a number, it will be decreased to its 90%. What is the number ?**- 120
- 150
- 180
- 225
- None of these
**When 30 is subtracted from a number, it will be decreased to its 75%. What is the number ?**- 120
- 150
- 180
- 225
- None of these
**When 11.25 is subtracted from a number, it will be decreased to its 95%. What is the number ?**- 120
- 150
- 180
- 225
- None of these

__:__

**Model 13****When 135 is subtracted from a number, it will be decreased to its 11/20. What is its 75% ?**- 360
- 300
- 225
- 210
- None of these

**Solution :**

*x*- 135 = (11/20)

*x*

x - (11x/20) = 135

9x = 135 x 20

=> x = 300

75% = 300 x (75/100) = 225

__:__

**Practice Problems on Model 13****When 135 is subtracted from a number, it will be decreased to 17/20. What is its 40% ?**- 360
- 300
- 225
- 210
- None of these
**When 135 subtracted from a number, it will be decreased to its 31/40. What is its 35 % ?**- 360
- 300
- 225
- 210
- None of these
**When 240 is subtracted from a number, it will be decreased to its 7/15. What is its 66 2/3 % ?**- 360
- 300
- 225
- 210
- None of these

__:__

**Model 14**- When 2/7 of a number is added to 25, it becomes the number itself. What is its 175 % ?
- 35
- 42
- 40
- 70
- None of these

**Solution :**

(2

*x*/7) + 25 =*x*
(2

*x*/7) -*x*= 25
-5

*x*= 175*x*= 35

120% of the number = 35 x (120/100) = 42

__:__

**Practice Problems on Model 14****When 3/8 of a number is added to 25, it becomes the number itself. What is its 175% ?**- 35
- 42
- 40
- 70
- None of these
**When 4/9 of a number is added to 20, it becomes the number itself. What is its 116 2/3 % ?**- 35
- 42
- 40
- 70
- None of these
**When 3/7 of a number is added to 16, it becomes the number itself. What is its 125 % ?**- 35
- 42
- 40
- 70
- None of these

**:**

__Model 15__**The difference between 2/3 and 3/4 of a number is 15. What is the number ?**- 180
- 240
- 320
- 360
- None of these

**Solution :**

(2x/3) - (3x/4) = 15

=> (2x-3x) / 12 = 15

=> x = 180

__:__

**Practice problems on Model 15****The difference between 3/5 and 5/6 of a number is 56. What is the number ?**- 180
- 240
- 320
- 360
- None of these
**The difference between 5/12 and 7/15 of a number is 18. What is the number ?**- 180
- 240
- 320
- 360
- None of these
**The difference between 5/8 and 3/5 of a number is 8. What is the number ?**- 180
- 240
- 320
- 360
- None of these

__:__

**Model 16****A boy is asked to multiply a number by 2/5. By mistake he divided the number by 2/5 and got the answer 420 more than what he should have got if he had multiplied the number by 2/5. What is the number given to him ?**- 200
- 210
- 250
- 300
- None of these

**Solution :**

5

*x*/2 = (2*x*/5) + 420
(5

*x*/2) - (2*x*/5) = 420
= 25

*x*-4*x*= 4200
21

*x*= 4200
=>

*x*= 200__:__

**Practice Problems on Model 16****A boy is asked to multiply a number by 2/7. By mistake he divided the number by 2/7 and got the answer 675 more than what he should have got if he had multipled the number by 2/7. What is the number given to him ?**- 200
- 210
- 250
- 300
- None of these
**A boy is asked to multiply a number by 7/15. BY mistake he multiplied the number by 5/17 and got the answer 220 less than what he should have got if he had multiplied the number by 7/15. What is the number given to him ?**- 200
- 210
- 250
- 300
- None of these
**A boy is asked to multiply a number by 7/18. By mistake he multiplied the number by 8/17 and got the answer 125 more than what he should have got if he had multiplied the number by 7/18. What is the number given to him ?**- 200
- 240
- 250
- 300
- None of these

__:__

**Model 17****3/4 of a number is 160 less than its 80%. What is the number ?**- 320
- 480
- 3200
- 4800
- None of these

**Solution :**

3/4 => (3/4) x 100 = 75%

75% is 5% less than 80%

=> 5% ---> 160

+> 100% ----->

**320**__:__

**Practice Problems on Model 17****9/13 of a number is 154 less than its 80%. What is the number ?**- 320
- 480
- 3200
- 1430
- None of these
**3/5 of a number is 72 less than its 75%. What is the number ?**- 320
- 480
- 3200
- 4800
- None of these
**9/11 of a number is 132 more than its 75%. What is the number ?**- 320
- 480
- 3200
- 4800
- None of these

__:__

**Model 18****A number exceeds its 4/9 by 25. What is the number ?**- 36
- 48
- 54
- 63
- None of these

**Solution :**

x - (4/9) x = 25

9x - 4x = 225

5x = 225 => x = 45

__:__

**Problems on Model 18****A number exceeds its 5/12 by 28. What is the number ?**- 36
- 48
- 54
- 63
- None of these
**A number exceeds its 5/9 by 16. What is the number ?**- 3648
- 54
- 63
- None of these
**A number exceeds its 2/9 by 14. What is the number ?**- 36
- 48
- 54
- 63
- None of these

That's all for today friends. I will share more models tomorrow. Happy Learning :)