Question

Sakshi can do a piece of work in \[20\] days. Tanya is \[25\% \] more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
A.15
B.16
C.18
D.25

Answer 1

Hint: We will find the number of days taken by Tanya to complete the piece of work. We will find the ratio of the time taken by Sakshi and Tanya by using the relation between the time and efficiency and the ratio of the time taken by the given number of days and by equating these ratios, we will find the number of days. Thus, the number of days taken by Tanya to complete the piece of work.

Formula Used:
Time taken is always inversely proportional to the efficiency i.e., \[t \propto \dfrac{1}{{{\text{efficiency}}\% }}\]

Complete step-by-step answer:
We are given that Sakshi can do a piece of work in \[20\] days.
We are given that Tanya is \[25\% \] more efficient than Sakshi.
Let Sakshi efficiency be \[100\% \] then Tanya efficiency be \[125\% \]
We know that time is always inversely proportional to the efficiency i.e., \[t \propto \dfrac{1}{{{\text{efficiency}}\% }}\]
So, the Ratio of the time taken by Sakshi to Tanya \[ = \dfrac{1}{{100}}:\dfrac{1}{{125}}\] 
Now, by cross multiplying, to equalize the denominator, we get
\[ \Rightarrow \] Ratio of the time taken by Sakshi to Tanya \[ = 125:100\]
By simplification, we get
\[ \Rightarrow \] Ratio of the time taken by Sakshi to Tanya \[ = 5:4\] …………………………………………………………………\[\left( 1 \right)\]
Let \[x\] be the number of days taken by Tanya and Sakshi takes \[20\] days to complete the piece of work.
\[ \Rightarrow \] Ratio of the time taken by Sakshi to Tanya \[ = 20:x\] ……………………………………………………………….\[\left( 2 \right)\]
Now, by equating equation \[\left( 1 \right)\] and equation \[\left( 2 \right)\], we get
\[ \Rightarrow 5:4 = 20:x\]
Now, Ratio is represented in the form of Fractions, we get
\[ \Rightarrow \dfrac{5}{4} = \dfrac{{20}}{x}\]
By cross multiplying, we get
\[ \Rightarrow 5x = 20 \times 4\]
Now, by rewriting the equation, we get
\[ \Rightarrow x = \dfrac{{20 \times 4}}{5}\]
By simplifying the terms, we get
\[ \Rightarrow x = 4 \times 4\]
\[ \Rightarrow x = 16\]
Therefore, the number of days taken by Tanya to complete the piece of work is \[16\] days. So, Option (B) is the correct answer.

Note: We know that when two ratios are equal, then it is said to be in Proportion. So, \[5:4 = 20:x\] can also be written as \[5:4::20:x\]. When two quantities are in direct proportion, then when one amount increases, then another amount also increases at the same rate. So, we can write as \[x = y\]. When two quantities are in indirect proportion, then when one amount increases, then another amount decreases at the same rate. So, it can be written as \[x = \dfrac{1}{y}\] . We should remember these formulas while writing a proportion with direct and indirect variation. We should also know the relation between time and efficiency.