# A Problem (and Solution) from Bhaskaracharya’s Lilavati

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.
$$\dfrac {3n+3n \times \dfrac{3} {4} } {7} – \dfrac {1} {3} \times \dfrac {3n+3n \times \dfrac{3} {4} } {7} = 14$$
Now as we have:
$$\dfrac {n} {2} = 14$$
Thus the number is 28 .

##### Gaurav Tiwari
Gaurav Tiwari is a professional graphic & web designer from New Delhi, India. gauravtiwari.org is his personal space where he writes on blogging, digital marketing, content writing, learning and business growth. Gaurav has contributed in developing more than 325 brands worldwide and while you are reading this, he's busy building a couple more.

1. Super Q and A

2. i was searching for the answer and i got it here. Thank you:)

3. Loki gubbi

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

4. prateek

what a problem it is?

5. Srinath kesav

6. ajay gole

fantastic try to give more examples please from indian ancient maths

• sanjya

not good

• Hmmm. 😀

• I’ll be providing more such content very soon. 🙂 Better you try the Archives https://gauravtiwari.org/a/ for related posts.

• asmi

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

7. jayaprakash

I want learn lelawathi ganith

8. Kaushik

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 $$dfrac {3n+3n times dfrac{3} {4} } {7} – dfrac {1} {3} times dfrac {3n+3n times dfrac{3} {4} } {7} = 14$$
Now as we have:
$$dfrac {n} {2} = 14$$
Thus the number is 28 .

9. Kaushik

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. .

10. sumisha

What a nice problem?

11. ranjith

Nice solution

12. Vikas Ghode

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

13. Vishnu

Mera Bharath Mahaan…….

14. asmi

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