(i) The cost of a notebook is twice the cost of a pen. Consider the cost of a notebook to be ₹t and that of a pen to be ₹p. Charlie wrote t = 2p, whereas Meera wrote p = 2t. Which of these two representations is correct?
(ii) In a one-day International Cricket match between India and Sri Lanka played in Nagpur, two Indian batsmen together scored 176 runs. Manisha expressed this situation as x + y = 176, where the number of runs scored by one batsman is x, and the number of runs scored by the other is y. Is this a correct representation?
- (i) The cost of a notebook is twice the cost of a pen. Consider the cost of a notebook to be ₹t and that of a pen to be ₹p. Charlie wrote t = 2p, whereas Meera wrote p = 2t. Which of these two representations is correct?
- (ii) In a one-day International Cricket match between India and Sri Lanka played in Nagpur, two Indian batsmen together scored 176 runs. Manisha expressed this situation as x + y = 176, where the number of runs scored by one batsman is x, and the number of runs scored by the other is y. Is this a correct representation?
Step-by-step solution
Idea: Translate the sentence word by word. “Notebook is twice the pen” means notebook = 2 × pen. Test any equation with sample numbers: if a pen costs ₹10, a notebook must cost ₹20.
(i) The cost of a notebook is twice the cost of a pen. Consider the cost of a notebook to be ₹t and that of a pen to be ₹p. Charlie wrote t = 2p, whereas Meera wrote p = 2t. Which of these two representations is correct?
- “Cost of notebook = 2 × cost of pen” becomes t = 2 × p, i.e. t = 2p. This is Charlie’s equation.½ mark
- Test with numbers: pen ₹10 → notebook ₹20. Charlie: 20 = 2 × 10 ✓. Meera: 10 = 2 × 20? ✗. Meera’s equation says the pen costs twice the notebook. So Charlie is correct.½ mark
(ii) In a one-day International Cricket match between India and Sri Lanka played in Nagpur, two Indian batsmen together scored 176 runs. Manisha expressed this situation as x + y = 176, where the number of runs scored by one batsman is x, and the number of runs scored by the other is y. Is this a correct representation?
- Runs of first batsman + runs of second batsman = 176, so x + y = 176.½ mark
- Yes, Manisha’s equation is correct. It is a linear equation in two variables; pairs such as (100, 76) or (88, 88) are possible solutions (whole numbers from 0 to 176).½ mark
Check: (i) With p = 15, Charlie gives t = 30: the notebook is twice the pen ✓. (ii) If the scores were 92 and 84, then 92 + 84 = 176 ✓.
Answer to write in the exam
(i)
Cost of notebook = 2 × cost of pen
⇒ t = 2p
∴ Charlie’s representation is correct; Meera’s p = 2t is wrong
(ii)
Runs of one batsman + runs of the other = 176
∴ x + y = 176 is a correct representation
Common mistakes that cost marks
- Writing the numbers in the same order as the words “twice … pen” and getting p = 2t. Always test with a simple number.
- Thinking x + y = 176 is wrong because it does not tell us each score. An equation can be correct and still have many solutions.
How this can come in the exam
The length l of a hall is 3 m more than twice its breadth b. The equation is
- b = 2l + 3
- l = 2b − 3
- l = 2b + 3
- 2l = b + 3
Show answer
(C) l = 2b + 3
Length = 2 × breadth + 3, so l = 2b + 3.
A bag costs ₹50 more than three times the cost of a pouch. Taking the bag as ₹b and the pouch as ₹q, write the equation and check it for a pouch costing ₹40.
Show answer
b = 3q + 50 (1 mark). For q = 40: b = 120 + 50 = ₹170 (1 mark).Try one yourself
The number of girls g in a class is 5 less than the number of boys b. Write the equation.
Show answer
g = b − 5 (or b − g = 5).
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