I was reading a book on ancient mathematics problems from Indian mathematicians. Here I wish to share one problem from Bhaskaracharya‘s famous creation Lilavati.

### Problem

A beautiful maiden , with beaming eyes, asks of which is the number that multiplied by 3 , then increased by three-fourths of the product, divided by 7, diminished by one-third of the quotient, multiplied by itself, diminished by 52, the square root found, addition of 8, division by 10 gives the number 2 ?

Ahh.. Isn’t it very long sentenced problem? The solution is here:
The method of working out this problem is to reverse the whole process — Multiplying 2 by 10 (20), deducting 8 (12), squaring (144), adding 52 (196), ‘multiplied by itself’ means that 196 was found by multiplying 14 to itself.
Now, Let the number be n.

Then applying initial part of the problem on it.
$$\dfrac {3n+3n \times \dfrac{3} {4} } {7} – \dfrac {1} {3} \times \dfrac {3n+3n \times \dfrac{3} {4} } {7} = 14$$
14 is what we already had in first half of solution.
Now as we have:
$$\dfrac {n} {2} = 14$$
Thus the number is 28 .

##### 18 comments
1. i was searching for the answer and i got it here. Thank you:)

2. Loki gubbi says:

Waw, this is an interesting problem with beautiful soln. What a knok from bhaskara! I realy hats of u . What a great indian! Thanks

3. prateek says:

what a problem it is?

4. Srinath kesav says:

Thanks for the Answer

5. ajay gole says:

fantastic try to give more examples please from indian ancient maths

1. sanjya says:

not good

1. asmi says:

hi can u pls solve the equation step by step
thank u
🙂

6. jayaprakash says:

I want learn lelawathi ganith

7. Kaushik says:

Its a very good question but i didn’t understand how u got the answer? The first half is clear but didn’t understand the second part which is $$dfrac {3n+3n times dfrac{3} {4} } {7} – dfrac {1} {3} times dfrac {3n+3n times dfrac{3} {4} } {7} = 14$$
14 is what we already had in first half of solution.
Now as we have:
$$dfrac {n} {2} = 14$$
Thus the number is 28 .

8. Kaushik says:

Its a very good question but i didn’t understand how u got the answer? The first half is clear but didn’t understand the second half. If u can please show it in a better way. .

9. sumisha says:

What a nice problem?

10. ranjith says:

Nice solution

11. Vikas Ghode says:

The long expression you posted in above post is called First Expression(FE). I got another first expression which cannot be solved using fast tricks. But one you got can be solved easily(by assuming (3n+3n X (3/4))/ 7 to be another variable y) then I gets y-1/3y = 14
Solving it you will get y = 21
Put that y in FE original FE then you will get 28

12. Vishnu says:

Mera Bharath Mahaan…….

13. asmi says:

hi can u pls solve the equation step by step
thank u
🙂

This site uses Akismet to reduce spam. Learn how your comment data is processed.

## Real Sequences

Sequence of real numbers A sequence of real numbers (or a real sequence) is defined as a function…

## How Many Fishes in One Year? [A Puzzle in Making]

This is a puzzle which I told to my classmates during a talk, a few days before. I…
Read More

## Abel Prize for 2014 to Yakov Sinai

Mathematical Physicist Yakov Gregory Sinai, (b. 21st September 1935, 78 years old) has been awarded the prestigious Abel…

## Understanding Poincaré Conjecture

Introduction & Statement of Poincaré Conjecture In 1904, the french Mathematician Henri Poincaré posed an epoch-making question in…

## The Lindemann Theory of Unimolecular Reactions

[ Also known as Lindemann-Hinshelwood mechanism. ] It is easy to understand a bimolecular reaction on the basis…
Read More

## Dirichlet’s Theorem and Liouville’s Extension of Dirichlet’s Theorem

Topic Beta & Gamma functions Statement of Dirichlet’s Theorem \$ \int  \int  \int_{V}  x^{l-1} y^{m-1} z^{n-1} dx  dy…