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RD Sharma Solutions Class 8 Mathematics Solutions for Direct and Inverse Variations Exercise 10.1 in Chapter 10 - Direct and Inverse Variations

Question 16 Direct and Inverse Variations Exercise 10.1

11 men can dig 6 ¾ metre long trench in one day. How many men should be employed for digging 27 metre long trench of the same type in one day?

Answer:

Let’s consider number of men required be ‘x’ men

(27/4)/11 = 27/x

By cross-multiplying

x27/4 = 27(11)

x27/4 = 297

x = (297 × 4)/27

= 44

∴ To dig 27m long trench of same type in one day requires 44 men

Video transcript
"Student and Sunita Nile from Edo learning. I'm going to help you with your homework problem that is in front of me. Let me read it out. 11 men can dig 6 and 3/4 meter long trench in one day how many men should be employed for digging a 27 meter long trench of the same type in one day. So let us put a the information that we have in this table, which is drawn below. So here I shall write. The length Of the trench in meters As the heading and you know that I shall write number. Of Men So let's put in the information that we have. 11 Min so I will put their 11 here 11 men can take a 6 and 3/4 meter long trench in one day. So the length of the trench is 6 and 3/4 meter. The question is how many men so I put a question mark here how many men should be employed for digging a 27 meter long trench of the same type in one day. Okay, so we can see. That there is An element of proportionality here The thing is if you have a longer Trench. You will need more men to dig it. Because the trenches of the same type and the time given is also Wendy. So a longer trench will need more men. If a trench of 6 and 3/4 meter needs 11 men naturally a trench of 27 meter length will require moment. So we can say that the ratio of the length of the trench to the number of men. Is fixed in both in both the situations. So let's write down those ratios 6 and 3/4. Is 211 is the first ratio and 27 is 2X. Is our second ratio and we say that these two ratios are in proportion. That means these two ratios are equal. So now I haven't dated in the fractional form. 6 and 3/4 / 11 Is equal to I can replace the proportionality sign by an equal sign is equal to 27 upon X. Now before we proceed further, let's convert the 6 and 3/4 into a improper fraction. So I will do it here. 6 and 3/4 Is equal to 4 x 6 that is 24 plus 3 is 27 a bond for If so, I will replace my six and three-quarter by 27 upon 4 So I will write it here now 27 upon for / 11 is equal to 27 / X Now the room when you have two fractions being equal to each other. The rule of cross multiplication applies So the that rule is if upon B is equal to C upon d It Why's that? A into D is equal to Be in to see so applying that rule here. We will get 27 upon 4 into X is equal to 27 in 211. So transposing 27 upon for to the other side of the equal sign. We get X is equal to 27 into 11 divided by 27 a point for Which works out to? 27 in to 11 now when I have to divide by a fraction. I have to mull it works out, too. Multiplying by the reciprocal of that fraction. It's so I have it here. Into for upon 27, right? So when I have to divide by this fraction All I have to do is multiply by the reciprocal of it multiply by its reciprocal. Simplifying this term further. I see that I can. Cancel this 27 with the 27 in the denominator. So I'm left with Lavin into 4, which equals 44 so my X is equal to 44 I have my X is equal to 44. The number of men required to dig the 27 meter trench of the same type in one day is 44. So my answer is 44 Men So they are problem is solved. To drop a comment in the comment section if this video has helped you understand the solution to the problem. Visit our YouTube channel regularly, you will find many more such homework solutions being explained subscribe to our channel for updates as well. Thank you."
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