Question

I brought 30 books on Mathematics, Physics, and Chemistry, priced at Rs.17, Rs.19, and Rs.23 per book respectively, for distribution among poor students of Standard X of a school. The physics books were more in number than the Mathematics books but less than the Chemistry books, the difference being more than one. The total cost amounted to Rs.620. How many books on Mathematics, Physics, and Chemistry could have been bought respectively?

• A. 5, 8, 17
• B. 5, 12, 13
• C. 3, 5, 10, 15
• D. 4, 5, 6, 19

Hint:

When dealing with word problems involving total sums and relationships between variables, setting up system of equations can help narrow down the correct solution.

Answer 1

The Correct Option is B

Let the number of Mathematics, Physics, and Chemistry books be denoted by \(x\), \(y\), and \(z\) respectively. From the problem, we know: \[ x + y + z = 30 \text{(total number of books)} \] The total cost is Rs.620, so the cost equation is: \[ 17x + 19y + 23z = 620 \text{(total cost)} \] We are also given that \(y>x\) and \(z>y\), with the difference between the numbers being more than one. This helps us limit the possible values of \(x\), \(y\), and \(z\). Solving these two equations, we get: \[ x = 5, y = 12, z = 13 \] Thus, the correct number of books is \(5\) Mathematics, \(12\) Physics, and \(13\) Chemistry books.