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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

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

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
10 days ago
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∝1efficiency% 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∝1efficiency% So, the Ratio of the time taken by Sakshi to Tanya =1100:1125 Now, by cross multiplying, to equalize the denominator, we get ⇒ Ratio of the time taken by Sakshi to Tanya =125:100 By simplification, we get ⇒ Ratio of the time taken by Sakshi to Tanya =5:4 …………………………………………………………………(1) Let x be the number of days taken by Tanya and Sakshi takes 20 days to complete the piece of work. ⇒ Ratio of the time taken by Sakshi to Tanya =20:x ……………………………………………………………….(2) Now, by equating equation (1) and equation (2) , we get ⇒5:4=20:x Now, Ratio is represented in the form of Fractions, we get ⇒54=20x By cross multiplying, we get ⇒5x=20×4 Now, by rewriting the equation, we get ⇒x=20×45 By simplifying the terms, we get ⇒x=4×4 ⇒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=1y . We should remember these formulas while writing a proportion with direct and indirect variation. We should also know the relation between time and efficiency.

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