{"id":28789,"date":"2025-06-20T15:33:30","date_gmt":"2025-06-20T15:33:30","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=28789"},"modified":"2025-06-20T15:33:32","modified_gmt":"2025-06-20T15:33:32","slug":"if-10-mens-working-7-hours-a-day-to-get-range-147-m-long-how-many-men-working-8-hours-a-day-will-be-get-range-160-m-long-of-the-same-breadth-and-depth-as-the-first-in-the-same-number-of-days","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/if-10-mens-working-7-hours-a-day-to-get-range-147-m-long-how-many-men-working-8-hours-a-day-will-be-get-range-160-m-long-of-the-same-breadth-and-depth-as-the-first-in-the-same-number-of-days\/","title":{"rendered":"If 10 men’s, working 7 hours a day to get range 147 M long how many men working 8 hours a day will be get range 160 M long (of the same breadth and depth as the first in the same number of days)?"},"content":{"rendered":"\n
If 10 men’s, working 7 hours a day to get range 147 M long how many men working 8 hours a day will be get range 160 M long (of the same breadth and depth as the first in the same number of days)?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
To solve this, we use the concept of man-hours, which is the product of the number of men, the number of hours worked per day, and the number of days. Since the work is directly proportional to the man-hours and the range (length) of the trench, we can set up a proportion to solve the problem.<\/p>\n\n\n\n
Given:<\/h3>\n\n\n\n
\n
10 men working 7 hours a day can dig a trench of length 147 meters.<\/li>\n\n\n\n
We need to find how many men working 8 hours a day are required to dig 160 meters of trench in the same number of days.<\/li>\n<\/ul>\n\n\n\n
Let the number of men required be x<\/strong>.<\/p>\n\n\n\n
Work done is proportional to:<\/p>\n\n\n\n
\n
Number of men \u00d7 Hours per day \u00d7 Number of days \u221d Length of trench<\/p>\n<\/blockquote>\n\n\n\n
Let the number of days be D<\/strong> (same in both cases), and the breadth and depth remain the same (so the amount of earthwork is proportional to length only).<\/p>\n\n\n\n
Case 1:<\/strong> Work = 10 men \u00d7 7 hours\/day \u00d7 D days = 70D man-hours Trench length = 147 meters<\/p>\n\n\n\n
Case 2:<\/strong> Work = x men \u00d7 8 hours\/day \u00d7 D days = 8xD man-hours Trench length = 160 meters<\/p>\n\n\n\n
Now set up the proportion:70D147=8xD160\\frac{70D}{147} = \\frac{8xD}{160}14770D\u200b=1608xD\u200b<\/p>\n\n\n\n
Cancel D<\/strong> from both sides:70147=8×160\\frac{70}{147} = \\frac{8x}{160}14770\u200b=1608x\u200b<\/p>\n\n\n\n
Approximately 10 men<\/strong> are needed (rounding up to the nearest whole number since you cannot have a fraction of a person).<\/p>\n\n\n\n\n\n\n\n
Explanation <\/h3>\n\n\n\n
This problem involves a comparison of two similar work scenarios where the total work output is directly proportional to the combined labor and time spent. The idea is that if a certain number of men working a set number of hours per day can complete a task in a certain time frame, then altering any one of those variables will change the total manpower needed for a similar task in a proportional way.<\/p>\n\n\n\n
In this specific problem, we are comparing two trench-digging tasks. Both tasks are to be completed in the same number of days, and the trench’s breadth and depth remain constant. Therefore, the total volume of soil to be removed is proportional to the trench length. This simplifies the comparison to a ratio of trench lengths.<\/p>\n\n\n\n
We begin by calculating the effective man-hours in the first case (10 men working 7 hours a day), which gives us a base understanding of how much work is required to dig 147 meters. In the second case, we use a variable x to represent the unknown number of men working 8 hours a day. We assume both groups work the same number of days.<\/p>\n\n\n\n
By setting up a proportion between the man-hours and trench lengths of both cases, we solve for x, which gives us a decimal value. Since the number of men must be a whole number, we round up. This ensures that the work will be completed within the required timeframe without falling short due to an insufficient workforce.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
If 10 men’s, working 7 hours a day to get range 147 M long how many men working 8 hours a day will be get range 160 M long (of the same breadth and depth as the first in the same number of days)? The Correct Answer and Explanation is: To solve this, we use […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-28789","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28789","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=28789"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28789\/revisions"}],"predecessor-version":[{"id":28791,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28789\/revisions\/28791"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=28789"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=28789"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=28789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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