Question 14 of 17intermediate🔧 ApplyNumerical3 marks

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?

Correct Answer

Given: Let g = Gauri's cows Let n = Naina's cows

Equations: From 'Naina has twice as many': n = 2g From 'if Naina gave 3 to Gauri, they would be equal': n - 3 = g + 3

Substitution: 2g - 3 = g + 3

Solving: 2g - g = 3 + 3 g = 6

Finding n: n = 2g = 2(6) = 12

Answer: Gauri has 6 cows and Naina has 12 cows.

Exercise: Figure it Out (Section 3) | Q: 8 | (Page Page 12)
For More Understanding

Explanation

Using algebra: Let g = Gauri's cows, n = Naina's cows. From first statement: n = 2g. From second statement: if Naina gives 3 cows to Gauri, they have equal numbers, so n - 3 = g + 3. Substituting n = 2g: 2g - 3 = g + 3, giving g = 6 and n = 12.

Solution Steps

  1. Step 1: Let g = Gauri's cows, n = Naina's cows

  2. Step 2: From 'Naina has twice as many': n = 2g

  3. Step 3: From 'if Naina gave 3 to Gauri, they would be equal': n - 3 = g + 3

  4. Step 4: Substitute: 2g - 3 = g + 3

  5. Step 5: Solve: g = 6

  6. Step 6: Therefore n = 12

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