Question

Write a multiplication table of 27 using Vinculum method and identify the number at sixth place.
$\left( a \right)$ 108
$\left( b \right)$ 135
$\left( c \right)$ 162
$\left( d \right)$ 270

Answer 1

Hint: In this particular type of question use the concept that if the number is not ending with zero then we have to write the number which is the difference of the nearest number ending with zero and a single digit number so that the resultant is original number so use this concept to reach the solution of the question.

Complete step-by-step answer:
Now we have to find out the multiplication table of 27 using the Vinculum method.
So as we see that the given number is not ending with zero.
So it is written as the difference of the nearest integer ending with zero and the single digit number so that it gives us the resultant number.
So the nearest integer ending with zero and corresponding to 27 is 30.
So we have to subtract 3 from 30 so that resultant is 27.
Therefore, 27 = (30 – 3).
Now it is easier to calculate the multiplication table of 27 using this method.
So the multiplication table of 27 is given below,

Original number27	Number written according to Vinculum method, 27 = (30 – 3)	Resultant value after multiplication
1(27)	1(30 – 3)	27
2(27)	2(30 – 3)	60 – 6 = 54
3(27)	3(30 – 3)	90 – 9 =81
4(27)	4(30 – 3)	120 – 12 = 108
5(27)	5(30 – 3)	150 – 15 = 135
6(27)	6(30 – 3)	180 – 18 = 162
7(27)	7(30 – 3)	210 – 21 = 189
8(27)	8(30 – 3)	240 – 24 = 216
9(27)	9(30 – 3)	270 – 27 = 243
10(27)	10(30 – 3)	300 – 30 = 270

So this is the required multiplication table according to the Vinculum method.
So as we see from the table the number at sixth place is 162.
So this is the required answer.

Note – Whenever we face such types of question always recall how to find the multiplication table using vinculum method which is stated above, if the last digit of the given number is less than five (consider 24) then according nearest integer ending with zero is 20 so in this we have to add 4 to get the resultant number, therefore, 24 = (20 + 4), so overall if the last digit is greater than 5 then we apply difference rule and if the last digit is less than five then we apply addition rule and if last digit is 5 then we apply any rule.