Example 5 - Chapter 8 Class 7 - Working with Fractions (Ganita Prakash)

Transcript

Example 5 This problem was posed by Chaturveda Pṛithūdakasvāmī (c. 860 CE) in his commentary on Brahmagupta’s book Brāhmasphuṭasiddhānta. Four fountains fill a cistern. The first fountain can fill the cistern in a day. The second can fill it in half a day. The third can fill it in a quarter of a day. The fourth can fill the cistern in one fifth of a day. If they all flow together, in how much time will they fill the cistern? Let us solve this problem step by step. In a day, the number of times — • the first fountain will fill the cistern is 1 ÷ 1 = 1 • the second fountain will fill the cistern is 1 ÷ 1/2 = _____ • the third fountain will fill the cistern is 1 ÷ 1/4 = _____ • the fourth fountain will fill the cistern is 1 ÷ 1/5 = _____ The number of times the four fountains together will fill the cistern in a day is ___ + ____ + ___ + ____ = 12. In a day, the number of times, First fountain will fill the cistern is = 1 ÷ 1 = 1 times Second fountain will fill the cistern is = 1 ÷ 1/2 = 1 ×2/1 = 2 times Third fountain will fill the cistern is = 1 ÷ 1/4 = 1 ×4/1 = 4 times Fourth fountain will fill the cistern is = 1 ÷ 1/5 = 1 ×5/1 = 5 times Thus, The number of times the four fountains together will fill the cistern in a day is 1 + 2 + 4 + 5 = 12.