Question

Mangoes are sold at \[Rs.\]\[43\dfrac{1}{2}\] per kg. What is the weight of mangoes available for \[Rs.\]\[326\dfrac{1}{4}\]?

Answer 1

Hint: The one of the ways to solve it by using formulas for finding weight.
Then we do some simplification to get the answer.
Also we have to change the mixed number into improper fraction for that
Finally, we can get the answer easily.

Formula used: \[{\text{Weight of mangoes (in kg) = }}\dfrac{{{\text{Total price available}}}}{{{\text{ Price of mangoes}}\left( {{\text{in 1kg}}} \right)}}\]

Complete step-by-step answer:
It is given that \[1kg\] of mangoes \[ = Rs.43\dfrac{1}{2}\]
Let the required weight be named as ‘\[x\]’
So we can write it as, \[x kg\] of mangoes \[ = Rs.326\dfrac{1}{4}\]
Now, we change the mixed number to proper fraction
First, we take that \[Rs.43\dfrac{1}{2}\],
On multiply, the denominator of the fraction by the whole number
That is we can write it as,
Denominator is \[2\] whole number is \[43\], \[43 \times 2 = 86\]
 Let us add this product to the numerator of the fraction.
That is we can write it as,
Numerator is \[1\], \[86 + 1\] = \[87\]
The sum is the numerator of the improper fraction.
Here, the denominator of the improper fraction is the same as the denominator of the fractional part of the mixed numbers. Therefore, the numbers are \[\dfrac{{87}}{2}\],
\[\therefore Rs.43\dfrac{1}{2} = Rs.\dfrac{{87}}{2}\]
Also we take \[Rs.326\dfrac{1}{4}\].
On multiply, the denominator of the fraction by the whole number
That is we can write it as,
Denominator is \[4\] whole number is \[326\], \[326 \times 4 = 1304\]
 Let us add this product to the numerator of the fraction.
That is we can write it as,
Numerator is \[1\], \[1304 + 1\] = \[1305\]
The sum is the numerator of the improper fraction.
Here, the denominator of the improper fraction is the same as the denominator of the fractional part of the mixed numbers. Therefore, the numbers are \[\dfrac{{1305}}{4}\]
\[\therefore Rs.326\dfrac{1}{4} = Rs.\dfrac{{1305}}{4}\]
Now, we use the formula,
\[{\text{Weight of mangoes (in kg) = }}\dfrac{{{\text{Total price available}}}}{{{\text{ Price of mangoes}}\left( {{\text{in 1kg}}} \right)}}\]
Here the data are,
Total price available is \[Rs.\dfrac{{1305}}{4}\]
Price of \[1kg\] mangoes is \[Rs.\dfrac{{87}}{2}\]
Substitute the value in the formula
Weight of mangoes (in\[xkg\]) = \[\dfrac{{\dfrac{{1305}}{4}}}{{\dfrac{{87}}{2}}}\]
The denominator of the fraction is taken reversal and it is multiplied
\[\dfrac{{1305}}{4} \times \dfrac{2}{{87}} = x\]
Cancel \[4\] by \[2\]
\[\dfrac{{1305}}{2} \times \dfrac{1}{{87}}\]=\[x\]
We can write \[1305\] as \[1305\] = \[15 \times 87\]
\[\dfrac{{15 \times 87}}{2} \times \dfrac{1}{{87}}\]=\[x\]
Cancel numerator \[87\] by denominator \[87\]
We get,
\[\dfrac{{15}}{2}\] = \[x\]
\[x\] = \[7.5\]
Here, \[x\] is the weight of mangoes in the unit of kg,
$\therefore $ \[x\] = \[7.5\] kg of mangoes for \[Rs.\dfrac{{1305}}{4}\] or
\[x\] = \[7.5\] kg of mangoes for \[Rs.326\dfrac{1}{4}\]

Note: If you notice here the weight is increased, the price is also increased.
And the weight is decreasing, the price is also decreasing.
This is called direction, by using the relation we get the answer.