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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

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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
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.
S
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