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?
Solution:- Fixed charge = ₹x
Charge per km = ₹y
Case (i): For a distance of 10 km, the charge paid is ₹105,
∴ Fixed charge + 10(Charge per km) = 105
∴ x + 10y = 105
∴ x = 105 - 10y ------- (i)
Case (ii): For a distance of 15 km, the charge paid is ₹155,
∴ Fixed charge + 15(Charge per km) = 155
∴ x + 15y = 155
∴ 105 - 10y + 15y = 155 { from (i) }
∴ 15y - 10y = 155 - 105
∴ 5y = 50
∴ y =
50
/
5
∴ y = 10
*Putting y = 10 in Eqⁿ(i)
∴ x = 105 - 10(10)
∴ x = 105 - 100
∴ x = 5
Therefore,
Fixed charge = ₹x = ₹5
Charge per km = ₹y = ₹10
➙ Amount paid by a person for travelling a distance of 25 km,
= Fixed charge + 25(Charge per km)
= 5 + 25(10)
= 5 + 250
= ₹255
Therefore, the person have to pay ₹255 for travelling a distance of 25 km.
Hence,
The fixed charge is ₹5 and the charge per km is ₹10 and a person have to pay ₹255 for travelling a distance of 25 km.
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Try This..
✒ A shopkeeper sells a pen for ₹50 and a notebook for ₹80. If he sold 10 pens and some notebooks for ₹1,300, how many notebooks did he sell?
✒ The sum of two numbers is 60 and their difference is 20. Find the numbers.
✒ A boat takes 2 hours to go downstream and 3 hours to come back upstream. If the speed of the stream is 2 km/h, find the speed of the boat in still water.
❌ Common Mistakes
Wrong assignment of variables:▸ Always define what each variable stands for clearly (e.g., fixed charge and per km rate).Missing units:▸ Don’t forget to write ₹ for prices and km for distances.Calculation errors:▸ Be careful when solving equations; one small subtraction mistake can throw off your answer.Forgetting to substitute back:▸ After finding one variable, always substitute it back to get the other.
📝 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 (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.
- 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 iv Class 10
Class 10 Ex 3.2 Q3 iv
Class 10 Chap 3 Ex 3.2 Q3 iv
Class 10 Pair Of Linear Equations in Two Variables
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