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Rs. 480 is divided equally among 'x' children. If the number of children were 20 more, then each would have got Rs. 12 less. Find 'x'. - ICSE Class 10 - Mathematics

Question

Rs. 480 is divided equally among 'x' children. If the number of children were 20 more, then each would have got Rs. 12 less. Find 'x'.

Solution

Total amount = Rs. 480
Let the number of children be x.
The amount each children got = 480/"x"
when the number of children were 20,
amount of each children = 480/("x"+20)
From the given information, we have:

480/"x"-480/("x"=12)=12

(480"x"+480xx20-480"x")/("x"("x"+20))=12

9600/("x"("x"+20))=12

800/("x"("x"+20))=1

x2 + 20x - 800 = 0
x2 + 40x - 20x - 800 = 0
x(x + 40) - 20(x + 40) = 0
(x - 20)(x + 40) = 0
x = 20, -40
Since, number of children cannot be negative. So, x = 20
Number of children = 20

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Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6E | Q: 16

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Solution Rs. 480 is divided equally among 'x' children. If the number of children were 20 more, then each would have got Rs. 12 less. Find 'x'. Concept: Quadratic Equations.
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