Question

Apples are sold at $Rs.{\text{48}}\dfrac{4}{5}$ per kg. What is the cost of $3\dfrac{3}{4}$ kg of apples?

Answer 1

Hint: In this question the cost of one kg apple is given and the cost of the required amount of apples can be found out by unitary method. Also change the mixed-fraction terms in the normal fraction so that the solution seems to be easy.

Complete step-by-step solution:
Cost of 1kg of apple= $48\dfrac{4}{5}$
As we know the mixed-fraction of the form $a\dfrac{b}{c}$ can be written as $\dfrac{{a \times b + c}}{c}$ .
$\therefore {\text{ 48}}\dfrac{4}{5} = \dfrac{{48 \times 5 + 4}}{5}$
On simplifying further
$ \Rightarrow 48\dfrac{4}{5} = \dfrac{{244}}{5}$
Also,
$Total{\text{ amount of apple = 3}}\dfrac{3}{4}$
$3\dfrac{3}{4}{\text{ is also of the form a}}\dfrac{b}{c}$
$\therefore {\text{ 3}}\dfrac{3}{4} = \dfrac{{3 \times 4 + 3}}{3}$
On simplifying further,
$ \Rightarrow 3\dfrac{3}{4} = \dfrac{{15}}{4}$
$\therefore {\text{ Cost of 1kg apple = }}\dfrac{{244}}{5}$
${\text{Total amount of apple = }}\dfrac{{15}}{4}$
From unitary method,
$\because {\text{ Cost of 1kg apple = }}\dfrac{{{\text{244}}}}{5}$
$\therefore {\text{ Cost of }}\dfrac{{15}}{4}kg{\text{ apples = }}\dfrac{{15}}{4} \times \dfrac{{244}}{5}$
$ \Rightarrow \operatorname{Cos} t{\text{ of }}\dfrac{{15}}{4}kg{\text{ apples = }}\dfrac{{15 \times 244}}{{4 \times 5}}$
On simplifying further,
${\text{Cost of }}\dfrac{{15}}{4}kg{\text{ apples = }}\dfrac{{3660}}{{20}}$
On dividing
${\text{Cost of }}\dfrac{{15}}{4}kg{\text{ apples = 183}}$
$\therefore {\text{ The total cost of }}\dfrac{{15}}{4}kg{\text{ apples is Rs}}{\text{.183}}$

Note: In this type of question it is always fruitful to change the mixed fraction terms to the normal fraction. It can also be solved by assuming the unknown to be some variable and after that solve for that variable. The units of the different quantities given in the question can sometimes be changed i.e. the given weight can be in kilograms but the solution asks for the amount to be in grams and vice-versa. The same happens for the other quantities as well. If the given quantities are in different units then change all the units to the same unit. If the given data is in decimal then it can be changed into fraction and solve it after that, or continue with the decimal value but remember to round up the answer. Substitute the values carefully to avoid any mistake. Do not make calculation mistakes so that the right answer would not come. Always try to solve the problem step by step.