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Problems On Numbers Questions for SSC, CDSE, CLAT and Railways Exams

Directions: Study the following questions carefully and choose the right answer.
1
The ratio between a two-digit number and the sum of the digits of that number is 4 : 1. If the digit in the unit's is three more than the digit in the ten's places, what is the number?

A
25
» Explain it
B
Let the ten's digit be x. then, unit's digit =  (x + 3).

Sum of the digits = x + (x + 3) = 2x + 3.

Let the number  = 10x + (x +3) = 11x + 3

So,  11x + 3   =  4
2x + 3 1

⇒  11x + 3  = 4(2x + 3)  ⇔  11x + 3  = 4 (2x + 3) 

⇒  3x  =  9    ⇒   x  =  3

Hence, required number =  11x + 3  ⇒  36.

Hence, option B is correct.

2
If three numbers are added in pairs, the sums equal 10, 19 and 21. Find the numbers?
» Explain it
C
Smart Approach:

By 'Hit & Trial' method
 
(2 + 3) ≠ 10. Option 'A' gets eliminated
 
(6 + 8) ≠ 10. Option 'B' gets eliminated too. 
 
(6 + 4) = 10
 
(4 + 15) = 19
 
& (15 + 6) = 21
 
It's evident that the numbers in option 'C' satisfy the given condition.
 
Hence, option 'C' is the correct answer.
_____________________________________________________________

Traditional Approach:

Let the numbers be x, y and z. then

x + y = 10      .....(1)     y + z = 19      .....(2)     x + z  =  21    ....(3)

Adding (1), (2) and (3),

we get : 2(x + y + z) = 50   or  (x + y + z) = 25.

Thus, x = (25 – 19) = 6;  y = (25 – 21) = 4;  z = (25 – 10) = 15.

Hence, the required numbers are 6, 4 and 15.

Hence, option C is correct.

3
50 is divided into two parts such that the sum of their reciprocal is 1/12 find the two parts.
» Explain it
B
For shortcut method kindly refer to the video.

Let the two parts be x and (50 – x).

Then,  1  +  1  =  1
x 50 – x 12

⇒     50 – x + x  =  1
x(50 – x) 12

⇒  x2 – 50x + 600 = 0  ⇒  (x – 30) (x – 20) = 0

⇒  x = 20  or x = 30

So, the parts are 30 and 20.

Hence, option B is correct.

4
If sum of two numbers is 50, one of them 2/5th of other one then the value of numbers?
» Explain it
D

Let's the first numeber is x so,
another number will be  2 x, then,
5

⇒   x +  2 x = 50
5

⇒    5x + 2x  = 50
5

⇒    7x  = 50  
5  

⇒   x =  250
7


Similarly,


Another number will be

=    2  ×  250  =  100
5 7 7

Hence, the numbers are  250 ,  100 .
7 7


Hence, option D is correct.

5
A number exceeds its two fifth by 75. The number is:
» Explain it
C
Let the number be x

As per the the equation,
 
x –  2 x = 75
5

∴      3 x = 75   ⇒   x = 125.
5

Hence option C is correct.