Question

Reema, Ruchi and Richa can make a painting in 15, 20 and 30 days, respectively. They undertake to make a painting for Rs.810. The share of Reema exceed that of Ruchi by
A. Rs.91
B. Rs.92
C. Rs.90
D. Rs.89

Answer 1

Hint: To solve this problem, we should know the concept of work done vs days problems. A person can complete the work in x days means that the person can do $\dfrac{1}{x}$ portion of the work in 1 day. Using this statement, we can calculate the work done by the persons individually. The total work done by all of them in one day is the sum of their individual works done by them. We can get the number of days they work together using the above statements. The product of the number of days and the work done per day by an individual gives the share of work done by them. We know that the share of work done multiplied to the total amount that is Rs.810 gives the amount received by the individual.

Complete step-by-step answer:
We are given that three individuals Reema, Ruchi and Richa can make a painting in 15, 20 and 30 days, respectively.
 A person can complete the work in x days means that the person can do $\dfrac{1}{x}$ portion of the work in 1 day.
Using this statement, we can write that
Reema can do $\dfrac{1}{15}$ portion of painting in 1 day.
Ruchi can do $\dfrac{1}{20}$ portion of painting in 1 day.
Richa can do $\dfrac{1}{30}$ portion of painting in 1 day.
We know that they three worked simultaneously on the painting. The total work done by all of them in one day is the sum of their individual works done by them.
Using this, we can write the work done collectively by them in one day as
Work per day $=\dfrac{1}{15}+\dfrac{1}{20}+\dfrac{1}{30}=\dfrac{4+3+2}{60}=\dfrac{9}{60}=\dfrac{3}{20}$
Using the above statements, we can write that these three can finish the painting in $\dfrac{20}{3}$ days collectively.
Every person works for $\dfrac{20}{3}$ days on the painting.
We know that a person who can finish $\dfrac{1}{x}$ portion of work in one day is working for $y$days means that he finishes $\dfrac{y}{x}$ portion of the work. Using this, we can write that
Reema does $\dfrac{1}{15}\times \dfrac{20}{3}=\dfrac{4}{9}$ portion of painting in $\dfrac{20}{3}$ days.
Ruchi does $\dfrac{1}{20}\times \dfrac{20}{3}=\dfrac{1}{3}$ portion of painting in $\dfrac{20}{3}$ days.
Richa does $\dfrac{1}{30}\times \dfrac{20}{3}=\dfrac{2}{9}$ portion of painting in $\dfrac{20}{3}$ days.
We know that the total amount given for the painting is Rs. 810. So, we can write that the individual amounts that everyone gets will be the product of the portion done by them and the total amount given for the painting.
Reema does $\dfrac{4}{9}\times 810=4\times 90=\text{Rs}.360$ for her work on painting.
Ruchi does $\dfrac{1}{3}\times 810=\text{Rs}\text{.27}0$ for her work on painting.
Richa does $\dfrac{2}{9}\times 810=2\times 90=\text{Rs}\text{.18}0$ for her work on painting.
We are asked the difference of the amounts received by Reema and Richa. We can calculate the difference as
$\text{Difference}=360-270=Rs.90$
$\therefore $The required difference in amounts is Rs.90. The answer is option-C.

So, the correct answer is “Option C”.

Note: If we observe the options, they are very close to each other. Any error in calculation leads to a wrong answer in these types of questions. Some students might make a mistake by considering that the total number of days will be the sum of the individual days. This is a blunder because of the basic understanding that the number of days should decrease with more people involved in the work.