# Aptitude - Problems on Numbers - Discussion

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"Act well your part; there all honor lies."
- Alexander Pope
9.

In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:

 [A]. 24 [B]. 26 [C]. 42 [D]. 46

Explanation:

Let the ten's digit be x.

Then, unit's digit = x + 2.

Number = 10x + (x + 2) = 11x + 2.

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

(11x + 2)(2x + 2) = 144

22x2 + 26x - 140 = 0

11x2 + 13x - 70 = 0

(x - 2)(11x + 35) = 0

x = 2.

Hence, required number = 11x + 2 = 24.

 Abc said: (Mon, Jul 5, 2010 07:34:28 AM) how did u get 10x here

 Mamta said: (Thu, Dec 23, 2010 02:10:08 AM) confusing... can it be little more simplified

 Bharathi said: (Mon, Feb 7, 2011 09:12:25 AM) How unit digit is x+2 ?

 Gupta said: (Sat, Feb 12, 2011 10:59:48 AM) In the question it is clearly mentioned that units digit is 2 more than tens digit, then by observing the options only in 24 units digit(i.e.4 ) is more than 2 with tens digit(i.e.2).

 Kranth said: (Fri, Feb 25, 2011 09:42:41 AM) Confusing in the answer. There is not clearence.

 Karthi said: (Mon, Feb 28, 2011 01:15:21 AM) It is confusing please explain about 10x.

 Soumya said: (Mon, Apr 25, 2011 01:30:18 PM) Explanation about 10x eg:123 means 100+20+3 in question its given tat unit's digit exceeds its ten's digit by 2 ,so units place is x+2 n tens place is 10x....

 Naresh said: (Fri, Jun 10, 2011 04:33:46 AM) Its not the case of confusing..its the case of time consuming...just check the options only two options may give the answer..24 and 46... now apply the second condition given in the problenm to these two options 24*(2+4)=144.. so this is the correct answer

 Sandeep said: (Fri, Sep 9, 2011 11:20:39 PM) Nice explanation naresh.

 Ashmis said: (Mon, Sep 19, 2011 09:24:39 PM) I just divided the 144 with the options. 144 is completely divided by 24 so that is the answer.

 Indu said: (Wed, Nov 30, 2011 01:13:40 PM) Please tell me why we do not take 10x+y here. Please sing 10x+y.

 Venkat said: (Wed, Jan 4, 2012 11:07:42 PM) If option A is correct according to naresh why not C, as it is same to a when we add up ?

 Shikha said: (Wed, Feb 6, 2013 02:04:29 PM) I don't get this step. Sum of digits = x + (x + 2) = 2x + 2. Why we added x instead of 10x to (x+2).

 Avdhesh said: (Mon, Feb 11, 2013 04:46:43 PM) @Venkat. We want the product of digit (ie. 24) and its sum (ie 2+4) = 144. And for option C number is 42 doesn't satisfy the condition.

 Avdhesh said: (Mon, Feb 11, 2013 04:48:55 PM) @Shikha. Hey if we add 10x to (x+2) we will get that number. And when we add x to (x+2) we get the sum so. Hope I clarify a bit.

 Posubabu said: (Sat, Aug 31, 2013 02:22:54 PM) Let the ten's digit be x. Then, unit's digit = x + 2. for Example: Take Number 56. Here unit digit is 6, ten's digit is 5, Then Number = 50(since its 10th digit)+6 = 56. Hence in the above case: Number = 10x+ (x+2) = 11x+2. The remaining same explained by indiabix.

 Nupur said: (Sat, Jan 18, 2014 06:24:17 PM) How did 11x2+13x-70 produces (x-2)(11x+35) factors?

 Shakthi said: (Fri, Apr 4, 2014 11:31:56 PM) Multiply a term(11) and c term (-70) = -770. Find two numbers that when multiplied equal the number (-770) and add up to be the b term (13). The numbers be -22 and 35. Now write this as, 11x2-22x+35x-70 = 0. 11x (x-2) +35 (x-2) = 0. The factors are x-2 and 11x-35. If I'm wrong, please explain me.

 Amrith said: (Mon, Aug 18, 2014 11:17:19 PM) First mutiple 11* -70 which gives product = -770 and sum = 13. Next factorise 770 number ,u will get 2*5*7*11...in this series try to make combination such that sum should be 13 and product should be -770. The combination which we get is by trial and error, is 5*7=35 and 2*11=22, hence we choose 35 and -22 to satisfy p=-770 and sum=13, Next substitute in equation, 11x^2+35x-22x+4=0. x(11x+35)-2(11x+35)=0. Hence, (x-2)(11x+35) = 0. Hence we get x = 2 and y = x+2 = 4.

 Sudharshan said: (Mon, Aug 10, 2015 07:47:22 PM) Find Two digit number which is 4 times of digits sum and 2 times of digits multiplication.

 Rohan said: (Sat, Sep 5, 2015 02:13:18 PM) Dear experts, Please solve the following problem: In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and if 18 is added with the number then the digits exchanges their position. Find the number with explanation. Here's the answer 24, but I need algebraic explanation. Thanks.

 Ayesha said: (Wed, Dec 30, 2015 01:27:01 AM) How x=2 and y=x+2=4 came?