Amisha bought a number of books for ₹ 1,800, If she had bought 10 more books for the same amount, each book would have cost her ₹ 30 less. How many books did she buy originally?
Answers
Answer:
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Answer:
Let the number of books bought be x.
Step-by-step explanation:
book will be =1200x+10+20=1200x+10+20……….(ii)
By solving equation (i) and (ii), we get
⇒1200x=1200(x+10)+20⇒1200x=1200(x+10)+20
⇒1200x−1200(x+10)=20⇒1200x−1200(x+10)=20
Take 1200 common in L.H.S, we get
⇒1200[1x−1(x+10)]=20⇒1200[1x−1(x+10)]=20
⇒[1x−1(x+10)]=201200⇒[1x−1(x+10)]=201200
⇒[1x−1(x+10)]=160⇒[1x−1(x+10)]=160
⇒(x+10)−xx(x+10)=160⇒(x+10)−xx(x+10)=160
On cross multiplying, we get
⇒600=x2+10x⇒600=x2+10x
⇒x2+10x−600=0⇒x2+10x−600=0
On splitting the middle term, we get
⇒x2+30x−20x−600=0⇒x2+30x−20x−600=0
⇒x(x+30)−20(x+30)=0⇒x(x+30)−20(x+30)=0
⇒(x−20)(x+30)=0⇒(x−20)(x+30)=0
⇒x=20,x=−30⇒x=20,x=−30
−30−30 is not possible because the number of books will be a natural number. Therefore, we only consider x=20x=20. So, the shopkeeper will purchase 20 books for rupees 1200.
Note: Students may take the second equation as 1200x+10−201200x+10−20 but, this will not give correct answer either we have to take 1200x+10+201200x+10+20 or we may take 1200x+101200x+10 and then first equation will become 1200x+10+201200x+10+20. On solving these 2 equations we will get the value of xx.