Question

Mrs.Sharma sold a jewellery at a loss of 5%. If he had sold it at Rs.5,200 more, she would have gained 8%. Find the cost price of the jewellery ?

Answer 1

`"cost price" =Rs40000`

A lot of detail given so that you can see where everything comes from.

Explanation:

`color(blue)("Modelling the given conditions")`

Set the original selling price as `x`
Let the cost price be `y`

`color(brown)("Consider the 5% loss condition. ")`

To get get just the cost price back we have `(100)/(100)xxy`

But what she got back was: `(100-5)/100xxy`

And we know this is the original selling price so we have:

`95/100ycolor(white)("d")=color(white)("d")xcolor(white)("dddd") =>color(white)("dddd") ycolor(white)("d")=color(white)("d")100/95 x" "..Equation(1)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Consider the 8% profit")`

To obtain this profit she sold it for Rs 5200 more than the original selling price of `x`. So we have:

`y+8%y=x+5200`

`y(1+8%)=x+5200`

`y(108/100)=x+5200`

`y=[(100/108)x]+[100/108xx5200]" "...Equation(2)`
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`color(blue)("Putting it all together")`

Substitute for `y` in `Equation(2)` using `Equation(1)`

`100/95 x=100/108x+[100/108xx5200]`

Subtract `100/108 x` from both sides

`(100x)/95-(100x)/108=(100xx5200)/108`

Lets make all the denominators the same so we need to change the 95 into 108.

Note that `95xx108/95 = 108` so by applying this we have:

`(100xx108/95xx x)/108-(100x)/108=(100xx5200)/108`

Multiply all of both sides by 108

`(100xx108/95xx x)-100x=100xx5200`

`10800/95 x-100x = 520000 larr" Using decimals will introduce"`
`color(white)("ddddddddddddddddddddddddd")"rounding errors so I am sticking"`
`color(white)("dddddddddddddddddddddddd")" with fractions"`

`260/19 x = 520000`

`x=520000xx19/260 = 38000`
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`color(blue)("Determine the cost price.")`

Using `Equation(1)`

`y=100/95 x color(white)("d")->color(white)("d")y=100/95xx38000`

`"cost price" =y=Rs40000`

color(white)("d")