Time and work [समय और काम] – 01

Question: 20 men can prepare 40 toys in 24 days working 18 hours a day. Then in how many days can 36 men prepare 48 toys working 16 hours a day. [20 पुरुष 18 घंटे प्रति दिन काम करते हुए 40 खिलौने को 24 दिनों में सकते हैं. तो, बताइए कि 36 पुरुषों को 16 घंटे प्रति दिन काम करते ही 48 खिलौने बनाने में कितने दिन लगेंगे?] [Ans. (d) 18 days]

(a) 16      (b) 12       (c) 21      (d) 18         (e) None of these

Solution:

Detailed Explanation: Out of any two of “Men” (working strength), “Days” (time period) and “Hours” (rate with respect to time) are inversely to each other, so they have same suffices; they are directly proportional to “Work”, so they have opposite suffices with respect to “Work”.   

First Method:  

Second Method: In this method, we always interchange the value of work and then cancel them. One thing must be remembered that the row containing question mark (?) should always in the denominator.

Third Method: This is fractional value method. In this method, we take two values at time out of which one must be that value, which is to be determined. In this question, “Days” (time) is to be determined, so we write question mark (?) for time = 24 days  and take one by one, other values.

The ratio of men is either 20/36, or 36/20. One of them is less than fraction (less than one) and the other is more than fraction (more than one). For more men (for 36 men instead of 20 men), the taken will be less, so we multiply by 20/36. For less rate (for 16 h/d instead of 18 h/d), no. of men will be more, so we multiply by 18/16. And again, for more work (for 48 toys instead of 40 toys), there will be required more time, so we multiply by 48/40. Thus, no. days required is