21 pencils and 29 pens cost Rs. 79. But, if the number of pencils and pens were interchanged, the cost would have reduced by Rs. 8. Find the cost of each pen.
Question
21 pencils and 29 pens cost Rs. 79. But, if the number of pencils and pens were interchanged, the cost would have reduced by Rs. 8. Find the cost of each pen.
Solution
Let's denote the cost of a pencil as 'p' and the cost of a pen as 'q'.
From the first statement, we can form the equation: 21p + 29q = 79
From the second statement, we can form the equation: 29p + 21q = 79 - 8 = 71
Now we have a system of two equations, and we can solve it step by step.
First, multiply the first equation by 29 and the second by 21, to make the coefficients of 'p' the same in both equations:
2921p + 2929q = 7929 2129p + 2121q = 7121
This gives us:
609p + 841q = 2291 609p + 441q = 1491
Now, subtract the second equation from the first:
609p + 841q - 609p - 441q = 2291 - 1491 400q = 800
Divide both sides by 400:
q = 800 / 400 = 2
So, each pen costs Rs. 2.
Similar Questions
If 6 pens and 7 pencils together cost Rs.90, while 5 pens and 6 pencils cost Rs.76, what will be the cost of each pen?
Cost of 2 pens, 5 pencils and 7 erasers is 37 rupees.Cost of 7 pens, 1 eraser and 2 pencils is 49 rupees.What is the cost of 9 pencils and 47 pens?*
Question No. 21DIRECTIONS for question 21: Select the correct alternative from the given choices.The cost of an eraser is one-twelfth of that of a pen and two-thirds of that of a pencil. If the cost of two pens is ₹33 more than the cost of five pencils, then find the cost of one pen, two pencils and three erasers.₹30₹36₹48₹33
. A pen and 12 erasers cost $17.70. A pen and 15 erasers cost $20.40. How much do 6 pens cost?
Ravi carried two types of pens with him. The ratio of cost of pen A: pen B was 10 : 4. There were two pens of type B with him and the average cost of all the three pens together was Rs.60/-. Find the cost of pen A.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.