360 Journal of the Asiatic Society of Bengal. [September, 1912. 
generally by Diophantus.! The solution given in the Bakhshali 
manuscript is as follows :— 
‘«The sum of the additive and subtractive numbers is 12, 
the half of it is 6, lessened by 2 is 4, its half 2, its square 4, 
which is added to the substractive number and becomes 11. 
This is the number.’’ This solution is based upon the fact 
2 
that (= —p } +a+bis a perfect square. See el-Karchi.? 
Sttra 53. A earns 5 daily and B earns ; - df A gives e 
to B when wiil they have equal amounts ? 
den es Te 
mn Wad 
6 ad 
le 1:—A earns 3 and B earns £. A gives 7 to B 
whence they will have equal amounts in 30 days. 
Stitra 54. ‘‘ With the sale the purchase should be divided ; 
then divide it again diminished by one, then multiply it with 
the profit. It is then the capital.’’ 
If the rate of cost is A and the sale price B and the total 
FP. 
Basi: 
aample :—‘* One purchases (at the rate of) seven for two 
and sells (at the rate of) six for three. Eighteen is his profit. 
ay now what is his capital ? ’’ 

profit P, then the capital is 
' Answer 24. 
rea ta 
Unnumbered Sutras and Examples. 
1. A gives x, B gives 2x, C gives 3a, D gives 4x. The 
total is 200. 
1+2+3+4=10 +99=20. 
Therefore 20 +40 +60+80=200 are the numbers. 
2. A gives x, B gives twice as much as A, C gives 3 times 
athe as iB, D gives 4 times as much as C, and the total 
is 132. 
If A gives 1, then B gives 2, C gives 6, D gives 24. 
1+2+6+24=33 w2=132=4. 
2 ii, ILE. 2 Woepcke, p. 63. 
