Question 14 - Figure it out - Page 185 to 189 - Chapter 7 Class 7 - Finding the Unknown (Ganita Prakash II)

Transcript

Question 14 The Bakhśhāli Manuscript (300 CE) mentions the following problem. The amount given to the first person is not known. The second person is given twice as much as the first. The third person is given thrice as much as the second; and the fourth person four times as much as the third. The total amount distributed is 132. What is the amount given to the first person? Let Amount given to 1st person = x Given that The second person is given twice as much as the first So, we can write Amount given to 2nd person = 2 × Amount given to 1st person = 2x Also, given that The third person is given thrice as much as the second; So, we can write Amount given to 3rd person = 3 × Amount given to 2nd person = 3 × 2x = 6x And again, given that The fourth person four times as much as the third So, we can write Amount given to 4th person = 4 × Amount given to 3rd person = 4 × 6x = 24x Finally, given that The total amount distributed is 132 Thus, we can write Amount with all 4 persons = 132 x + 2x + 6x + 24x = 132 x × (1 + 2 + 6 + 24) = 132 x × 33 = 132 Taking 33 to right side, it becomes division x = 𝟏𝟑𝟐/𝟑𝟑 x = 44/11 x = 4 Thus, amount given to the first person is 4