Question 36 - CBSE Class 10 Sample Paper for 2027 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

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Question 36 A student entrepreneur started a company that manufactures sanitizers in two sizes – small and large. The cost of a small bottle of sanitizer is ₹10 and that of a large bottle is ₹15. In June, the company sold 1000 bottles and recorded a total sale of ₹12,750. Seeing the increased demand, the company decided to increase the price of both sanitizer bottles by ₹2 each. In the next month, the company sold 2500 bottles and recorded a total sale of ₹34,250. Based on the above information, answer the following questions: (i) Form a linear equation in two variables representing the sale for June. Let Number of small bottles be x Number of large bottles be y Given that cost of a small bottle of sanitizer is ₹10 and that of a large bottle is ₹15. In June, the company sold 1000 bottles and recorded a total sale of ₹12,750 So, we can write Number of small bottles × Price of small bottle + Number of large bottles × Price of large bottle = 12,750 10x + 15y = 12,750 And, since total 10,000 bottles were sold Number of small bottle + Number of large bottle = 10,000 x + y = 10,000 …(1) …(2) Thus, our linear equation in two variables for June is 10x + 15y = 12,750 …(1) x + y = 1,000 …(2) Question 36 (ii) (ii) Form a linear equation in two variables representing the sale for July. Now, we are given that Seeing the increased demand, the company decided to increase the price of both sanitizer bottles by ₹2 each. In the next month, the company sold 2500 bottles and recorded a total sale of ₹34,250. Thus, Price of small bottle in July = 10 + 2 = ₹ 12 Price of large bottle in July = 15 + 2 = ₹ 17 Since total sales in July is ₹ 34,250 So, we can write Number of small bottles × Price of small bottle + Number of large bottles × Price of large bottle = 34,250 12x + 17y = 34,250 And, since total 2,500 bottles were sold Number of small bottle + Number of large bottle = 1,000 x + y = 2,500 Thus, our linear equation in two variables for July is 12x + 17y = 34,250 …(3) x + y = 2,500 …(4) …(3) …(4) Question 36 (iii) – (A) How many sanitizer bottles of each type were actually sold in June? We have to solve these equations 10x + 15y = 12,750 …(1) x + y = 1,000 …(2) From (2) x + y = 1,000 y = 1,000 – x Putting value of y in (1) 10x + 15y = 12,750 10x + 15(1,000 – x) = 12,750 10x + 15,000 – 15x = 12,750 15,000 – 5x = 12,750 15,000 – 12,750 = 5x 2,250 = 5x 5x = 2,250 x = (2,250)/(5) x = 450 Putting x = 450 in (2) x + y = 1,000 450 + y = 1,000 y = 1000 – 450 y = 550 Thus, Number of small bottles sold in June = x = 450 Number of large bottles sold in June = y = 550 15,000 – 5x = 12,750 15,000 – 12,750 = 5x 2,250 = 5x 5x = 2,250 x = (2,250)/(5) x = 450 Putting x = 450 in (2) x + y = 1,000 450 + y = 1,000 y = 1000 – 450 y = 550 Thus, Number of small bottles sold in June = x = 450 Number of large bottles sold in June = y = 550 Number of small bottles sold in June = x = 450 Number of large bottles sold in June = y = 550 Question 36 (iii) – (B) How many sanitizer bottles of each type were sold in July? We have to solve these equations 12x + 17y = 34,250 …(3) x + y = 2,500 …(4) From (4) x + y = 2,500 y = 2,500 – x Putting value of y in (3) 12x + 17y = 34,250 12x + 17(2,500 – x) = 34,250 12x + 42,500 – 17x = 34,250 42,500 – 5x = 34,250 42,500 – 34,250 = 5x 8,250 = 5x 5x = 8,250 x = (8,250)/(5) x = 1,650 Putting x = 1,650 in (4) x + y = 2,500 1,650 + y = 2,500 y = 2,500 – 1,650 y = 850 Thus, Number of small bottles sold in July = x = 1,650 Number of large bottles sold in July = y = 850 42,500 – 5x = 34,250 42,500 – 34,250 = 5x 8,250 = 5x 5x = 8,250 x = (8,250)/(5) x = 1,650 Putting x = 1,650 in (4) x + y = 2,500 1,650 + y = 2,500 y = 2,500 – 1,650 y = 850 Thus, Number of small bottles sold in July = x = 1,650 Number of large bottles sold in July = y = 850 Number of small bottles sold in July = x = 1,650 Number of large bottles sold in July = y = 850