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 .

Posted by Gaurav Tiwari

Excellent Reader, Good Orator and Bad Writer. Talk about WordPress, PHP and Mathematics. I develop & design web applications that are visually brilliant and mass-friendly. I can also design stunning graphics to support my web-apps & amazing logos to amaze people. I have worked with several companies & individuals to deliver satisfactory results.

14 Comments

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

    Reply

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

    Reply

  3. what a problem it is?

    Reply

  4. Srinath kesav June 7, 2013 at 6:09 pm

    Thanks for the Answer

    Reply

  5. fantastic try to give more examples please from indian ancient maths

    Reply

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

      Reply

  6. I want learn lelawathi ganith

    Reply

  7. 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 .

    Reply

  8. 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. .

    Reply

  9. What a nice problem?

    Reply

  10. Nice solution

    Reply

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