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

Gaurav Tiwari

A designer by profession, a mathematician by education but a Blogger by hobby. With an experience of over seven years with WordPress, PHP and CSS3, Gaurav is capable of doing almost anything related to these. Beyond that, He is a mathematics graduate & a civil service aspirant.

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16 Responses

  1. Vidhya Cgr says:

    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

  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…….

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