# Problems on Numbers with Solutions

The basic problem with us is, we all are get used to the simple life. We want things appear to be simpler. If we find the question like what will be the value of (2/3)*(1/5)*(3/7)*5, we just solve it in a fraction of seconds. But if we come across the questions like what will be the two third of one fifth of three seventh of five then we just skip to the next question. Where is problem? The problem is with our mindset. All of us keep on telling our minds that these questions are hard. But trust me guys, these are very simple problems to solve. All that you have to do is, to just put your mind on the problem. Here, with this post we are giving you some problems that appears to be harder at first glance but really very simple to solve. These are very important for any competitive exam. All the best and Happy Reading :)

1. If two third of one fifth of three seventh of a number is 4, what is the number?
Solution :

Two Third of X is nothing but (2/5)X
One Fifth of X is nothing but (1/5)X
Three Seventh of X is nothing but (3/7)X

So, here two third of one fifth of three seventh of a number is 4, that means

2.  If three fifth of two seventh of a number is 24, what is its 40% ?
Solution :

here we need 40% cent of the number.

40 per cent means (40/10)th of the given number.

So, (40/100)*140 = 56 is the required answer.

3. If three fourth of two third of a number is 12, what is the sum of its digits?
Solution:

(3/4)*(2/3)*X = 12
So we get the number X = 24

the sum of its digits is 2+4 = 6

4. Two third of the first number is same as three fourth of the second number. What is their ratio ?
Solution :
Generally people tend to find out first and second numbers at first and later will find out their ratios. But there is a simple technique to solve these type of problems.

say First number is F and the second number is S,

given that (2/3)*F = (3/4)*S

so, F/S = (3/4)*(3/2) = 9/8

what are you waiting for? the required ratio is 9:8  ;)      simple.. isn't it?

5. Sum of two digits number and the number obtained by interchanging the digits is 44. What is the sum of the digits of the number ?
Solution :
Assume that the two digits of the given number are X and
Given that,

So, the sum of the two digit number and the number obtained by interchanging the digits will be,

(10X+Y)+(10Y+X) = 44

=> 11X + 11Y = 44

so, X+Y = 4

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 ?
Solution :
Same process as above,

(10X+Y) - ( 10Y+X) = 36

10X + Y - 10Y - X = 36

=> 9X - 9Y = 36

X - Y = 4       so required answer is 4

7. Sum of a two digits number and the number obtained by interchanging the digits is 55. Which of the following could be the difference between the digits of the number ?
1. 2
2. 3
3. 4
4. 7
5. 8
Solution :

10X + 10Y + X = 55
11X + 11 Y = 55       =>       X+Y= 5

we know the sum of the two numbers (x+y) is 5 and we also know that the  Sum of a two digits number and the number obtained by interchanging the digits is 55

So, now we should check combinations of X+Y=5 , the combinations should be (1,4), (3,2)

Now we should check the second rule  Sum of a two digits number and the number obtained by interchanging the digits should be 55

According to this rule, we are getting numbers (32, 23), (14,41), (23, 32), (41, 14).
Just check the given multiple choice options in the exam and choose the suitable option.

According to the given options the answer should be 3. (The difference between numbers 1 and 4.

Some important points to keep in mind :
• 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 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.
8.  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?
Solution:

Given that, X+Y = 9          --------------------(1)

and 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 = 1       --------------------(2)

So, 2X = 10

=> X = 5

from (1), Y will be 4.

So the number is 54

9. When 45 is added to a number, it will be increased by 20%. What is the number ?
Solution:

Then number is increased by 20%. That means the number is becoming 100% + 20% = 120%

(X + 45) =  (120 /100) X

100X + 4500 - 120 X = 0

=> X = 225

Shortcut Method :

if we add 45, the number is increasing 20%

then how much should we add to make it 100 %??

20% ------ 45

100% -------- ???

here we should multiply 20 with 5 to get 100. So just multiply 45 with the same 5.

So you will get 45 X 5 = 225

10. When 20 is subtracted from a number, it will be decreased by its 25%. What is the number ?
Solution :

same logic
25% ----------- 20
100% ----------- ?

So, the answer is 20 X 4 = 80

That's all for now friends. In our next post we shall discuss some more typical problems on Numbers with detailed explanations. And one more thing, for the explanatory purpose we have clearly mentioned each and every step here. But its advisable to all these calculations mentally without using pen and paper. Initially you may find it little harder. But with practice you surely can do that. All the best :)

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1. GOOD WORK
TYPING MISTAKE AT Q-7

1. explain mistake

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I'm preparing for bank exams very seriously . As of now, I'm working with software company and have SAT and SUN holiday.
My study schedule is as :
Monday to Friday :
Daily min 2 hrs for Maths/ Quant
3 Hrs for Reasooning in a Week
1 hr for English in a Week

- SAT and SUN _
Total 8 Hrs for Math/Quant
2 hrs for Reasoning
1 hrs for G.K

- I want to crack Bank PO exam in one attempt at any cost. please let me know any additional things which can assist me to crack in one attempt.

Regards,
Sandy

1. Your preparation plan and dedication is really good Sandy. But it seems you are paying less attention to General Awareness. Ofcourse no need to prepare for it daily. But make a habit of reading news papers and noting important points in a notebook. Like achievements, awards, deaths, sports updates, who is who etc. And for Saturday and Sunday try to solve previous model papers of POs (You can get them from market). It will help you in doing better in the REAL exam. All the best.

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