If 24 workers can build a wall in 15 days, how many days will 8 workers take to build a similar wall

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If 24 workers can build a wall in 15 days one worker can build the wall in = 15*24 days

8 workers can build the wall in =

days

= = 45 days Result: 45 days

50% students answered this correctly

1. Ratio:

(i) The Ratio of a number a to another number b (b≠0) is a fraction ab and is written as a:b.

(ii) In the ratio a:b, the first term is a and the second term is b.

(iii) A Ratio is said to be in the simplest form if its two terms have no common factor other than 1.

(iv) The ratio of two numbers is usually expressed in its simplest form.

(v) The ratio of two quantities is an abstract quantity, i.e., it has no units in itself.

2. Proportion:

(i) An equality of two ratios is called a Proportion. If a∶b=c∶d, then we write a:b∷c:d.

(ii) The numbers a, b, c, d are in Proportion if the ratio of the first two is equal to the ratio of the last two, i.e., a∶b=c∶d.

(iii) If four numbers a, b, c, d are in Proportion, then a and d are known as Extreme terms and b and c are called Middle terms.

(iv) Four numbers are in Proportion if the product of extreme terms is equal to the product of middle terms, i.e., a:b∷c:d if and only if ad=bc.

(v) From the terms of a given proportion, we can make three more proportions.

3. Continued Proportion:

(i) If a∶b=b∶c, then a, b, c are said to be in Continued Proportion.

(ii) If a, b, c are in Continued Proportion, i.e., a:b∷b:c, then b is called the Mean Proportional between a and c.

4. Unitary Method:

(i) The method of finding first the value of one article from the value of the given number of articles and then the value of the required number of articles is called the Unitary Method.

(ii) More is the number of articles; more is the value.

(iii) Value of a given number of articles = (Value of one article) × (Number of articles)

(iv) Less is the number of articles; less is the value.

(v) Value of one article =Value of a given number of articlesNumber of articles

We can use the unitary method to get the best deal when buying commodities like sugar and find out which brand offers more quantity for less money. Watch thi...

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We use ratios to compare the quantities of items. What if sometimes ratios with the same and different units need to be compared? Watch this video to learn h...

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What is meant by proportion? This video explains how to form proportion from ratio to show the relationship between quantities and how to read a proportion.

Can you define the ratio? This video is about a DIY project that will teach you to create a model representing ratios and proportions! Watch it and learn!

24 workers can build a wall in 15 days. How many days will 9 workers take to build a similar wall?

Number of days taken by 24 workers to build a wall = 15 days

Number of days taken by 1 worker to build the wall = 15 × 24 = 360 days (less worker means more days)

Number of days taken by 9 workers to build the wall = `360/9` = 40 days

Concept: Concept of Proportion

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Page 2

40 men can finish a piece of work in 26 days. How many men will be needed to finish it in 16 days?

Number of men required to complete the work in 26 days = 40

Number of men required to complete the work in 1 day = 40 × 26 = 1040 men (less men more days)

Number of men required to complete the work in 16 days = `1040/16` = 65

Concept: Concept of Proportion

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Answer

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Hint: Here, we have the data that 24 workers are building a wall in 15 days, we have to find the number of days will 8 workers take to build a similar wall. We will use the formula $\dfrac{{{M}_{1}}{{D}_{1}}{{H}_{1}}}{{{W}_{1}}}=\dfrac{{{M}_{2}}{{D}_{2}}{{H}_{2}}}{{{W}_{2}}}$ , where M is number of men, D is number of days, H is number of hours per day and W is work done. We have to consider only M and D here. We have ${{M}_{1}}=24,{{D}_{1}}=15,{{M}_{2}}=8$ , substituting these we can find ${{D}_{2}}$ .

Complete step-by-step answer:

We will be using the manpower-time-work concept. According to this, we have $\dfrac{MDH}{W}=\text{constant}$ , where M is number of men, D is number of days, H is number of hours per day and W is work done. When we have two conditions given, this formula is extended as $\dfrac{{{M}_{1}}{{D}_{1}}{{H}_{1}}}{{{W}_{1}}}=\dfrac{{{M}_{2}}{{D}_{2}}{{H}_{2}}}{{{W}_{2}}}$ .In our question, we have to relate only the M and D terms since the rest, i.e H and W are the same for building a similar wall.Since we have been given that 24 workers can build in 15 days, we can write that ${{M}_{1}}=24,{{D}_{1}}=15$.Now, let us take the number of days which 8 workers will take to make a similar wall to be $\alpha $ . So, we can write that as ${{M}_{2}}=8,{{D}_{2}}=\alpha $ .Now applying the above formula, we have $24\times 15=8\times \alpha $$\Rightarrow \alpha =\dfrac{24\times 15}{8}$$=\dfrac{360}{8}=45$Hence, 8 workers take 45 days to build the similar wall.

So, the correct answer is “Option b”.

Note: There is a high possibility that students might apply the concept of unitary method for this question. So, they may consider that 1 worker will build in $\dfrac{15}{24}$ days, so, for 8 workers, the number of days will be $\dfrac{15}{24}\times 8=5$ days. But, this is not correct logically, how can less number of workers finish the same work in less number of days since other conditions are not changing. Do not make this mistake. So, for such questions, always use the work-time concept.