# SBI Clerk 2018 Coaching - Problems on Numbers (Shortcuts & Practice Tests)

Hello friends. Today's topic in SBI Clerks 2018 coaching is Problems on Numbers. 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 Shortcuts

Model 1 :
1. If two-third of one-fifth of three-seventh of a number is 4, what is the number ?
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 :
1. If three-fourth of four-ninth of three-fifth of a number is 16, what is the number ?
1. 60
2. 70
3. 75
4. 80
5. None of these
2. If three-seventh of seven-ninth of three-fourth of a number is 15, what is the number ?
1. 60
2. 70
3. 75
4. 80
5. None of these
3. If two-ninth of nine-fourteenth of 2 1/3 times of a number is 25, what is the number ?
1. 60
2. 70
3. 75
4. 80
5. None of these
Model 2 :
1. If three-fifth of two-seventh of a number is 24, what is its 40% ?
1. 56
2. 64
3. 120
4. 140
5. None of these
Solution :

Say the number is

(3/5)  × (2/7) × n = 24

=> = 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 :
1. If four-fifth of five sixth of a number is 120, what is its 66 2/3 % ?
1. 56
2. 64
3. 120
4. 140
5. None of these
2. If three seventh of seven-fifteenth of a number is 84, what is its 33 1/3 % ?
1. 56
2. 64
3. 120
4. 140
5. None of these
3. If eighteen-nineteenth of 4 3/4 times of a number is 128, what is its 225% ?
1. 56
2. 64
3. 120
4. 140
5. None of these
Model 3 :
1. If three-fourth of two-third of a number is 12, what is the sum of its digits ?
1. 12
2. 8
3. 7
4. 5
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 :

1. If three-fourth of two-third of 65% of a number is 156, what is the sum of its digits ?
1. 12
2. 8
3. 7
4. 5
5. None of these
2. If nine-thirteenth of five-sixth of 62.5% of a number is 225, what is the sum of its digits ?
1. 12
2. 8
3. 7
4. 5
5. None of these
3. If seven-twelfth of three-eighth of 84% of a number is 147, what is the sum of its digits ?
1. 12
2. 8
3. 7
4. 5
5. None of these
Model 4 :

1. Two-third of the first number is same as three-fourth of the second number. What is their ratio ?
1. 8:9
2. 6:7
3. 9:8
4. 7:6
5. 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 :

1. Three-fourth of the first number is same as 87.5% of the second number. What is their ratio ?
1. 8:9
2. 6:7
3. 9:8
4. 7:6
5. None of these
2. Three-fourth of the first number is same as two-third of the second number. What is their ratio ?
1. 8:9
2. 6:7
3. 9:8
4. 7:6
5. None of these
3. 7 times of the first number is same as six times of the second number. What is their ratio ?
1. 8 : 9
2. 6 : 7
3. 9 : 8
4. 7 : 6
5. None of these
Model 5 :
1. 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 ?
1. 4
2. 5
3. 6
4. 7
5. None of these
Solution :

This is a tricky question. Here, they asked the SUM of the digits of the number.

If the two digits are x and y
x is on 10s place and y is on units place => 10x+y

The number obtained by interchanging the digits is => 10y+x

So,

10x+y  + 10y+x = 44
=> 11x+11y = 44
=> x+y = 4

Practice Problems on Model 5 :
1. 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 ?
1. 4
2. 5
3. 6
4. 7
5. None of these
2.  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 ?
1. 4
2. 5
3. 6
4. 7
5. None of these
3. 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 ?
1. 4
2. 5
3. 6
4. 7
5. None of these
Model 6 :
1. 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 ?
1. 4
2. 5
3. 6
4. 7
5. None of these
Solution :

Here, they asked the difference.

So,

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

10x+y-10y-x = 36

=> 9x - 9y = 36

x-y = 4

Practice Problems on Model 6 :
1. 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 ?
1. 4
2. 5
3. 6
4. 7
5. None of these
2. 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 ?
1. 4
2. 5
3. 6
4. 7
5. None of these
3. 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 ?
1. 4
2. 5
3. 6
4. 7
5. None of these
Model 7 :
1. 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 ?
1. 2
2. 3
3. 4
4. 7
5. 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 :
1. 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. 1
2. 3
3. 4
4. 7
5. 8
2. 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. 1
2. 3
3. 5
4. 7
5. 8
3. 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. 1
2. 5
3. 4
4. 7
5. 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 :
1. 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 ?
1. 6
2. 8
3. 10
4. 12
5. 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 :
1. 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 ?
1. 6
2. 8
3. 9
4. 12
5. 14
2. 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 ?
1. 3
2. 5
3. 7
4. 9
5. 11
3. 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 ?
1. 7
2. 9
3. 11
4. 13
5. None of these
Model 9
1. 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 ?
1. 63
2. 36
3. 45
4. 54
5. 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 :
1. 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 ?
1. 63
2. 36
3. 45
4. 54
5. None of these
2. 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 ?
1. 63
2. 36
3. 45
4. 54
5. None of these
3. 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 ?
1. 63
2. 36
3. 45
4. 54
5. None of these
Model 10 :
1. When 45 is added to a number, it will be increased by 20%. What is the number ?
1. 225
2. 240
3. 270
4. 300
5. None of these
Solution :

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

that means 20% -----> 45

To get 100% you need to multiply 20 with 5

So, multiply with 5 on both sides,

100% ----- 45x5 = 225

225 is the answer

Practice problems on Model 10 :
1. When 81 is added to a number, it will be increased by 30%. What is the number ?
1. 225
2. 240
3. 270
4. 300
5. None of these
2. When 96 is added to a number, it will be increased by 40%. What is the number ?
1. 225
2. 240
3. 270
4. 300
5. None of these
3. When 75 is added to a number, it will be increased by 25%. What is the number ?
1. 225
2. 240
3. 270
4. 300
5. 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 :
1. When 20 is subtracted from a number. It will be decreased by its 25%. What is the number ?
1. 60
2. 75
3. 80
4. 96
5. None of these
Solution :
25% ------ > 20

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

Practice Problems on Model 11 :
1. When 30 is subtracted from a number, it will be decreased by its 50%. What is the number ?
1. 60
2. 75
3. 80
4. 96
5. None of these
2. When 18.75 is subtracted from a number, it will be decreased by its 25%. What is the number ?
1. 60
2. 75
3. 80
4. 96
5. None of these
3. When 38.4 is subtracted from a number, it will be decreased by its 40%. What is the number ?
1. 60
2. 75
3. 80
4. 96
5. None of these
Model 12 :
1. When 30 is subtracted from a number, it will be decreased to its 80%. What is the number ?
1. 120
2. 150
3. 180
4. 225
5. 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 :
1. When 18 is subtracted from a number, it will be decreased to its 90%. What is the number ?
1. 120
2. 150
3. 180
4. 225
5. None of these
2. When 30 is subtracted from a number, it will be decreased to its 75%. What is the number ?
1. 120
2. 150
3. 180
4. 225
5. None of these
3. When 11.25 is subtracted from a number, it will be decreased to its 95%. What is the number ?
1. 120
2. 150
3. 180
4. 225
5. None of these
Model 13 :
1. When 135 is subtracted from a number, it will be decreased to its 11/20. What is its 75% ?
1. 360
2. 300
3. 225
4. 210
5. 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 :
1. When 135 is subtracted from a number, it will be decreased to 17/20. What is its 40% ?
1. 360
2. 300
3. 225
4. 210
5. None of these
2. When 135 subtracted from a number, it will be decreased to its 31/40. What is its 35 % ?
1. 360
2. 300
3. 225
4. 210
5. None of these
3. When 240 is subtracted from a number, it will be decreased to its 7/15. What is its 66 2/3 % ?
1. 360
2. 300
3. 225
4. 210
5. None of these
Model 14 :
1.  When 2/7 of a number is added to 25, it becomes the number itself. What is its 175 % ?
1. 35
2. 42
3. 40
4. 70
5. None of these
Solution :
(2x/7) + 25 = x

(2x/7) - x = 25

-5x = 175

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

Practice Problems on Model 14 :
1. When 3/8 of a number is added to 25, it becomes the number itself. What is its 175% ?
1. 35
2. 42
3. 40
4. 70
5. None of these
2. When 4/9 of a number is added to 20, it becomes the number itself. What is its 116 2/3 % ?
1. 35
2. 42
3. 40
4. 70
5. None of these
3. When 3/7 of a number is added to 16, it becomes the number itself. What is its 125 % ?
1. 35
2. 42
3. 40
4. 70
5. None of these
Model 15 :
1. The difference between 2/3 and 3/4 of a number is 15. What is the number ?
1. 180
2. 240
3. 320
4. 360
5. None of these
Solution :
(2x/3) - (3x/4) = 15
=> (2x-3x) / 12 = 15

=> x = 180

Practice problems on Model 15 :
1. The difference between 3/5 and 5/6 of a number is 56. What is the number ?
1. 180
2. 240
3. 320
4. 360
5. None of these
2. The difference between 5/12 and 7/15 of a number is 18. What is the number ?
1. 180
2. 240
3. 320
4. 360
5. None of these
3. The difference between 5/8 and 3/5 of a number is 8. What is the number ?
1. 180
2. 240
3. 320
4. 360
5. None of these
Model 16 :
1. 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 ?
1. 200
2. 210
3. 250
4. 300
5. None of these
Solution :

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

= 25x -4x = 4200

21x = 4200

=> x = 200

Practice Problems on Model 16 :
1. 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 ?
1. 200
2. 210
3. 250
4. 300
5. None of these
2. 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 ?
1. 200
2. 210
3. 250
4. 300
5. None of these
3. 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 ?
1. 200
2. 240
3. 250
4. 300
5. None of these
Model 17 :
1. 3/4 of a number is 160 less than its 80%. What is the number ?
1. 320
2. 480
3. 3200
4. 4800
5. 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 :
1. 9/13 of a number is 154 less than its 80%. What is the number ?
1. 320
2. 480
3. 3200
4. 1430
5. None of these
2. 3/5 of a number is 72 less than its 75%. What is the number ?
1. 320
2. 480
3. 3200
4. 4800
5. None of these
3. 9/11 of a number is 132 more than its 75%. What is the number ?
1. 320
2. 480
3. 3200
4. 4800
5. None of these
Model 18 :
1. A number exceeds its 4/9 by 25. What is the number ?
1. 36
2. 48
3. 54
4. 63
5. None of these
Solution :
x - (4/9) x = 25
9x - 4x = 225
5x = 225 => x = 45
Problems on Model 18 :
1. A number exceeds its 5/12 by 28. What is the number ?
1. 36
2. 48
3. 54
4. 63
5. None of these
2. A number exceeds its 5/9 by 16. What is the number ?
1. 3648
2. 54
3. 63
4. None of these
3. A number exceeds its 2/9 by 14. What is the number ?
1. 36
2. 48
3. 54
4. 63
5. None of these
That's all for today friends. I will share more models tomorrow. Happy Learning :)