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 .

Feel free to ask questions, send feedback and even point out mistakes. Great conversations start with just a single word.

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## 18 comments

Super Q and A

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

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

what a problem it is?

Thanks for the Answer

fantastic try to give more examples please from indian ancient maths

not good

Hmmm. 😀

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

hi can u pls solve the equation step by step

thank u

🙂

I want learn lelawathi ganith

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 .

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. .

What a nice problem?

Nice solution

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

Mera Bharath Mahaan…….

hi can u pls solve the equation step by step

thank u

🙂