Ex 3.2 Q3 (iii) - The coach of a cricket team buys 7 bats and 6 balls for ₹3800. Later, she buys 3 bats and 5 balls for ₹1750. Find the cost of each bat and each ball.
Solution:- Cost of one bat = ₹x
Cost of one ball = ₹y
Case (i): The coach buys 7 bats and 6 balls for ₹3800,
∴ 7(Cost of a bat) + 6(Cost of a ball) = 3800
∴ 7x + 6y = 3800
∴ 7x = 3800 - 6y
∴ x =
3800 - 6y
/
7
------- (i)Case (ii): The coach buys 3 bats and 5 balls for ₹1750,
∴ 3(Cost of a bat) + 5(Cost of a ball) = 1750
∴ 3x+ 5y = 1750
∴ 3(
3800 - 6y
/
7
) + 5y = 1750 --- {from (i)} ∴ 3(3800 - 6y) + 5y × 7 = 1750 × 7
∴ 11400 - 18y + 35y = 12250
∴ 35y - 18y = 12250 - 11400
∴ 17y = 850
∴ y =
850
/
17
∴ y = 50
➙ Putting y = 50 in Eqⁿ(i)
∴ x =
3800- 6(50)
/
7
∴ x =
3800 - 300
/
7
∴ x =
3500
/
7
∴ x = 500
Therefore,
Cost of one bat = ₹x = ₹500
Cost of one ball = ₹y = ₹50
Hence,
The cost of each bat and each ball is ₹500 and ₹50 respectively.
------------------------------------
Try This..
✒ A shopkeeper buys 5 notebooks and 3 pens for ₹145. Later, he buys 3 notebooks and 2 pens for ₹85. Find the cost of each notebook and pen.
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❌ Common Mistakes
Incorrect variable substitution:▸ Always check which variable you're solving for.Sign errors:▸ Be extra careful with subtraction in elimination method.Skipping steps:▸ Always show all steps in exams to get full marks; even if it seems simple.Calculation mistakes:▸ Double-check your multiplication and division when working with large numbers.
📝 Related Questions:-
- Ex 3.2 Q2 - Solve 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of ‘m’ for which y = mx + 3.
- Ex 3.2 Q3 (i) - The difference between two numbers is 26 and one number is three times the other. Find them.
- Ex 3.2 Q3 (ii) - The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
- Ex 3.2 Q3 (iv) - The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹105 and for a journey of 15 km, the charge paid is ₹155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
- Ex 3.2 Q3 (v) - A fraction becomes 9/11, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.
- Ex 3.2 Q3 (vi) - Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
Queries Solved:-
Class 10 Ex 3.2
Ex 3.2 Q3 iii Class 10
Class 10 Ex 3.2 Q3 iii
Class 10 Chap 3 Ex 3.2 Q3 iii
Class 10 Pair Of Linear Equations in Two Variables
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