Question

Two-third of a consignment was sold at a profit of 5% and the remaining at a loss of 2%. If the total profit was Rs. 400, find the value of the consignment.
A). 10000
B). 12000
C). 15000
D). 20000

Answer 1

Hint: When we say one-fourth of something, it is expressed in the form of \[\dfrac{1}{4}\]. By this, we get to know that the first part of the term one-fourth i.e. one, becomes the numerator and fourth i.e. the number 4 becomes the denominator. This is the way every fraction is expressed in its numerical form.
A percentage is denoted by a \[\% \] sign. When we talk about \[x\% \] of some value y, then its numerical value is \[\dfrac{x}{{100}} \times y\]. Profit is always added and loss is always subtracted, by this we obtain the remaining amount, also regarded as the total profit.

Complete step-by-step solution:
Let the value of the consignment be represented as X.
To find: X
Given:
$\dfrac{2}{3} \times X \times \dfrac{5}{{100}}$ is the profit that is acquired after the consignment is sold.
And $\dfrac{1}{3} \times X \times \dfrac{2}{{100}}$ is the loss. The consignment is 1 as a whole, if two-third of it goes into profit, then two-third subtracted from 1 becomes the loss, i.e. one-third becomes the fraction considered for loss.
Therefore, the equation becomes,
$\Rightarrow \dfrac{2}{3} \times X \times \dfrac{5}{{100}} - \dfrac{1}{3} \times X \times \dfrac{2}{{100}} = 400$
LHS = $\dfrac{2}{3} \times X \times \dfrac{5}{{100}} - \dfrac{1}{3} \times X \times \dfrac{2}{{100}}$
     \[=X\dfrac{{10}}{{300}} - X\dfrac{2}{{300}}\]
     \[=\dfrac{8}{{300}}X\]
Equating LHS to RHS, we get \[\dfrac{8}{{300}}X = 400\]
Therefore, $X = 400 \times \dfrac{{300}}{8} = 15000$
Hence, from the given multiple choices – the C option is the correct answer.

Note: Read the question very carefully. After reading the question, which value is unknown and in what way we can find that value has to be clear. Interpreting the question into an equation has to be the important part of such sums. Once we form the equation, rest is just solving. Also, while adding or subtracting the fractions make sure that they have equal bases, if not, make the bases equal.