Last updated at May 29, 2018 by Teachoo

Transcript

Ex 3.7, 2 One says, Give me a hundred, friend! I shall then become twice as rich as you . The other replies, If you give me ten, I shall be six times as rich as you . Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II] [Hint : x + 100 = 2(y 100), y + 10 = 6(x 10)]. Let amount of money with first person = x and amount of money with second person = y When the first Person takes 100 from the second Person Money with first Person = x + 100 Money with Second Person = y 100 Given that, when first Person takes 100 from the second Person, he becomes twice as rich as the second person x + 100 = 2 (y 100) x + 100 = 2y 200 x 2y = 200 100 x 2y = 300 When the second Person takes 10 from the first Person Money with first Person = x 10 Money with second person = y + 10 Given that, when second person takes 10 from the first Person, he becomes 6 times as rich as the first person y + 10 = 6 (x 10) 6 (x 10) = y + 10 6x 60 = y + 10 6x y = 10 + 60 6x y = 70 Hence, the equations are x 2y = 300 (1) 6x y = 70 (2) From equation (1) x 2y = 300 x = 300 + 2y Putting x = 300 + 2y in equation (2) 6x y = 10 6( 300 + 2y) y = 70 1800 + 12y y = 70 11y = 70 + 1800 11y = 1870 y = 170 Putting y = 170 in equation (1) x 2y = 300 x (2 170) = 300 x 340 = 300 x = 40 Therefore, Amount of money with first person = x = 40 Amount of money with second person = y = 170

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.