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# A three digit number which on being subtracted from another three digit number consisting of …(CAT, 2013)

- May 14, 2018
- Posted by: allexamshelps
- Category: CAT

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1,721 total views, 1 views today

**Solution:**

**A three digit number which on being subtracted from another three digit number:**

**We know the concept of face values and place values.**

#### ( the face value only gives the numeric value of that number)

**So we can write a three-digit number following the method of place values.**

**100a+10b+c**

**On reversing the order, we have:**

**100c+10b+a**

**Since the question is saying that subtract from the reversed order**

**(A three-digit number which on being subtracted from another three digits number consisting of the same digits in reverse order gives 594)**

**On subtracting a three digit number from the same reversed order three-digit number, we get 594.**

**In equation form, it can be written:**

**(100c+10b+a) – (100a+10b+c ) = 594**

**Open the bracket:**

**100c+10b+a – 100a-10b-c = 594**

**Arranging by similar terms**

**(100c-c)+(10b-10b)+(a-100a) = 594**

**99c+0+(-99a)= 594**

**99c – 99a = 594**

**99 is the common multiplier in both terms i.e 99c and 99a. Hence, it will be taken out.**

**99(c-a) = 594**

** (c-a) = \frac { 594 }{ 99 }**

**(c-a) = 6**

**Hence the difference between c and a is 6, and c > a.**

**We know that digits can range from 0 to 9**

**0 cannot take the hundreds place like 023, otherwise, it will give us a two digit number.**

**From 1 to 9, we have to choose a value for ‘a’, the third digit, by maintaining a difference of 6 with c, the first digit.**

**If a=1 c can be 7**

**If a=2 c can be 8**

**If a=3 c can be 9**

**Since the question says find “the minimum possible sum of all the three digits…**

**The minimum value of a =1**

**B=0**

**C= 7**

**So, the sum is 1+0+7= 8**

** **

** **

** Hence the option (d) is correct.**

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