The Smart Teacher

Problem : The price of 3 buckets and 5 mugs is ₹ 100 and the price of 5 buckets and 2 mugs is ₹ 970. Find the price of one bucket and one mug separately. Solution : Suppose that the price of one bucket is ₹ x and price of one mug is ₹ y. therefore, the price of 3 buckets and 5 mugs = 3x+5y ₹ According to the first condition ₹ 3x+5y =1000 3x+5y = 1000 ............1 and price of 5 buckets and 2 mugs = ₹ 5x+2y According to the second condition ₹ 5x+2y = 970 so, 5x+2y = 970 ............2 Multiply by 5 both sides of the question 1 and by 3 in both sides of thr questio 2. 15x+25y = 5000 ..........3 15x+6y = 2910 ............4 Subtracting question 4 from the question 3 19y = 2090 y = 2090/19 or, y =110 Substituting the value of y in question 1 3x+5y = 1000 3x+ 5×110 = 1000 or, 3x+550 = 1000 3x = 1000-550 3x = 450 x = 450/3 x = 150 Hence price of one bucket = ₹ 150 and price of one mug = ₹ 110