Maths Shortcuts and Mind Tricks
To Solve Time and Work Related Problems
Q) If 3 men can do a piece of work in 6 days while 5 women can do the same work in 18 days Then find in how many days can 4 men and 10 women complete the same work together?
We have given:
Total Time taken by 3 men to do a work = 6 days
Total Time taken by 5 women to do same work = 18 dAYS
Normal Method to solve the above Problem:
Total work done by 3 men in 6 days = 3 × 6 = 18
Total work done by 5 women in 18 days = 5 × 18 = 90
Therefore,
1 day work of 1 Men will be = 1/18
1 day work of 1 Women will be = 1/90
So,
4 men can complete the work in 1 day = (4 × [1/18])
= [2/9]
10 women can complete the work in 1 day = (10 × [1/90])
= [1/9]
Therefore, (4 men + 10 women)’s 1 day work = 2/9 + 1/9
= (2+1)/9
=3/9
=1/3
Therefore, 4 men and 10 women can complete the work together in 3 days
Shortcut Method:
Total work done by 3 men in 6 days = Total work done by 5 women in 18 days is equal
i.e, 3 men × 6 days = 5 women × 18 days
18 men = 90 women
Therefore, 1 man = 5 women
As, 5 women = 1 man
Therefore, 10 women = 2 men
i.e 4 men + 10 women = 4 men + 2 men = 6 men
Therefore, Total No. of days taken by 4 men & 10 women together to complete the work = [18 men / 6 men]
= 3 days
Alternate Method:
We can also be solve the above problem by taking the number of women in consideration
As, 1man = 5 women
Therefore, 4 Men= 20 women
i.e 4 men + 10 women = 20 women + 10 women
= 30 women
So, no. of days taken by 4 men & 10 women to complete the work,
= [90 women / 30 women]
= 3 days.
THANK YOU
ALL THE BEST FOR EXAM
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