Question

Write a multiplication table of 39 using the Vinculum method and identify the number at $9^{th}$ place.
A) 312
B) 361
C) 390
D) 351

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 between the nearest number ending with zero and a single-digit number so that the result is the original number so use this concept to solve the question.

Complete step-by-step solution:
Now we have to find out the multiplication table of 39 using the Vinculum method.
So, as we see that the given number is not ending with zero.
Then, 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.
Now the nearest integer ending with zero and corresponding to 39 is 40.
So, we have to subtract 1 from 40 so that the resultant is 39.
Now it is easier to calculate the multiplication table of 39 using this method.
The multiplication table of 39 is given below,

Original Number, (39)	Number according to Vinculum method, (40 – 1)	Resultant value after multiplication
1 (39)	1 (40 – 1)	40 – 1 =39
2 (39)	2 (40 – 1)	80 – 2 = 78
3 (39)	3 (40 – 1)	120 – 3 = 117
4 (39)	4 (40 – 1)	160 – 4 = 156
5 (39)	5 (40 – 1)	200 – 5 = 195
6 (39)	6 (40 – 1)	240 – 6 = 234
7 (39)	7 (40 – 1)	280 – 7 = 273
8 (39)	8 (40 – 1)	320 – 8 = 312
9 (39)	9 (40 – 1)	360 – 9 = 351
10 (39)	10 (40 – 1)	400 – 10 = 390

This is the required multiplication table according to the Vinculum method.
So, as we see from the table the number at $9^{th}$ place is 351.

Hence, the option (D) is the correct answer.

Note: Whenever we face such types of question always recall how to find the multiplication table using the vinculum method which is stated above if the last digit of the given number is less than five (consider 24) then according to the 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 the last digit is 5 then we apply any rule.