Aptitude - Percentage - Discussion

It's Very Easy:

Here, the numbers from 1 to 70 have 1 or 9.
In the units digit?

So, we have 1 to 70.

1 or 9 - here 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Here, 14 are there;
14/70 × 100.
14/7 × 10.
(140/7) = 20.

Here, the answer is 20

Why the no. '10' is not included? Please explain to me.

How to know if we should take 1 or 70 to make 70 total numbers, like we could have written 13/68 to take a percentage?

Anyone, please explain.

Numbers from 1 to 70.

1 unit digit -> 1,11,21,31,41,51,61 -> 7 numbers.
9 unit digit -> 9,19,29,39,49,59,69 -> 7 numbers.

So, the total 1 and 9 unit digits is 14 numbers.
Now percentage;
14/70 * 100 = 20%.

1-10 = 2 available 1,9.
11-20 = 2 available 11,19.
21-30 = 2 available 21,29.
31-40 = 2 available 31,39.
41-50 = 2 available 41,49.
51-60 = 2 available 51,59.
61-70 = 2 available 61,69.
Q1/q2 ×100.
= 14/70 ×100
= 20.

The unit's digit (or ones digit) of a number is the digit in the farthest right position. It represents how many ones are in the number.

For example:
In the number 345, the unit's digit is 5.
In the number 82, the unit's digit is 2.
In the number 1090, the unit's digit is 0.
So, when looking for numbers with a specific unit's digit, you're checking the last digit of each number.

@All.

Here, In 1s digit there are 14 numbers with 1 and 9.

So 70% = 100.
14% = x.
Cross multiply.
70 (x) =14 (100).
X = 1400/70.
X = 20.

@All.

Here, they have incorrectly missed the number range from 11-20, which includes 10 numbers (not 2). The ranges from 1-70, which include a 1 or 9. 11, 12, 13, 14, 15, 16, 17, 18, 19 = 10. All from 1 - 70 have 2. Therefore the total sum = 22/70 which equates to 31%.

To find the percentage of numbers from 1 to 70 that have 1 or 9 in the unit's digit, we first identify all such numbers.

Numbers with 1 in the unit's digit:
1, 11, 21, 31, 41, 51, 61

Numbers with 9 in the unit's digit:
9, 19, 29, 39, 49, 59, 69

Each set has 7 numbers.

Combining both sets, we have:
1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69,
In total, there are 14 numbers from 1 to 70 with either 1 or 9 in the unit's digit.

Percentage = ( Number of desired numbers)/Total numbers × 100.
Percentage = (14/70)× 100 = 20%.
Therefore, 20% of the numbers from 1 to 70 have either 1 or 9 in the unit's digit.

!All.

Here, They asked 1 or 9, why all answers are included both 1 and 9, if we considered 1 or 9 only the percentage should be 10%.

Correct me, if I'm wrong.