Question 8 - Figure it out - Page 145-147 - Chapter 6 Class 8 - Algebra Play (Ganita Prakash II)

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Question 8 Two friends, Gauri and Naina, are cowherds. One day, they pass each other on the road with their cows. Gauri says to Naina, “You have twice as many cows as I do”. Naina says, “That’s true, but if I gave you three of my cows, we would each have the same number of cows”. How many cows do Gauri and Naina have?Let Number of cows with Gauri = g Given that Gauri says to Naina, “You have twice as many cows as I do” So, Number of cows with Naina = 2 × Number of cows with Gauri = 2g Also, given that Naina says, “That’s true, but if I gave you three of my cows, we would each have the same number of cows” We can write this as Number of cows with Naina now = Cows with Naina earlier – 3 = 2g – 3 And, Number of cows with Gauri now = Cows with Gauri earlier + 3 cows from Naina = g + 3 Given that their Numbers are now equal. So, we write Number of cows with Naina now = Number of cows with Gauri now 2g – 3 = g + 3 2g = g + 3 + 3 2g = g + 6 2g – g = 6 g = 6 Thus, Number of cows with Gauri = g = 6 Number of cows with Naina = 2g = 2 × 6 = 12 Given that their Numbers are now equal. So, we write Number of cows with Naina now = Number of cows with Gauri now 2g – 3 = g + 3 2g = g + 3 + 3 2g = g + 6 2g – g = 6 g = 6 Thus, Number of cows with Gauri = g = 6 Number of cows with Naina = 2g = 2 × 6 = 12