Lilavati (The Beautiful) of Bhaskaracharya

Meaning: O Lilavati! You who possess the pride of a sixteen-year-old’s intellect! If you are clever in arithmetic original: pāṭī-gaṇita, referring to mathematics performed on a board or slate specifically in addition and subtraction, then tell me: what is the total of 2 (two), 5 (five), 32 (thirty-two), 193 (one hundred ninety-three), 18 (eighteen), 10 (ten), and 100 (one hundred)? And when all these are added together, how much remains when the sum is subtracted from 10,000 (ten thousand)? || 1 ||

Statement: 2 | 5 | 32 | 193 | 18 | 10 | 100
Result of addition original: samyojanājjātam: 360.

Explanation: According to the previously mentioned rule, following the sequence, first sum all the digits in the units place:

When added—that is, 2 (two) and 5 (five) make 7 (seven), and 2 (two) make 9 (nine), and 3 (three) make 12 (twelve), and 8 (eight) make 20 (twenty). From this twenty, the unit digit 0 (zero) is placed in the units column, beneath the other unit digits. Then, the remaining 2 (two) from the tens place is held in memory a "carry" in modern terms, and the digits in the tens place are summed: 3 (three) and 9 (nine) make 12 (twelve), and 1 (one) makes 13 (thirteen), and 1 (one) makes 14 (fourteen). To this, the previously carried 2 (two) is added, making 16 (sixteen). From this, the 6 (six) is placed to the left of the zero in the tens column, resulting in 60. The remaining 1 (one) from the sixteen is held in memory, and the digits in the hundreds place are counted: 1 (one) and 1 (one) make 2 (two). To this, the previous 1 (one) is added, making 3 (three). This is placed to the left of the six in the hundreds column, resulting in 360. Thus, the sum is three hundred sixty; in this same manner, addition should be performed elsewhere.

Subtracted from ten thousand original: ayuta (10,000), the result is 9,640.

9910 This interlinear annotation appears to be a correction or an alternative calculation note in the manuscript.

Explanation: 10,000 was subtracted according to the previously mentioned rule. That is, in the units place:

When the unit-place zero was subtracted from the unit-place zero, only zero remained. That 0 was placed beneath the unit digits. Next, the digit in the tens place is also zero. Since 6 (six) cannot be subtracted from it, one hundred is taken from the hundreds place; however, since the hundreds and thousands places are also zero here, one ten-thousand original: ayuta is taken from the ten-thousands place. This is converted into ten thousands, of which 9 (nine) are left in the thousands place. From the remaining 1 (one) thousand, ten hundreds are made, of which 9 (nine) are left in the hundreds place. From the remaining one hundred, ten tens were made, from which 6 (six) tens were subtracted...