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Aptitude Shortcut methof For Time and Work Problems

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by September 20, 2015 Aptitude

TIME AND WORKtime work

QUESTION:
3 men can do a piece of work in 6 days while 5 women can do the same work in 18 days. In how many days can 4 men and 10 women do the work?

GIVEN:
Time taken by 3 men to do a work = 6 days
Time taken by 5 women to do a work = 18 days

SOLUTION:

NORMAL METHOD:
3 men’s total work in 6 days = 3 × 6 = 18
5 women’s total work in 18 days = 5 × 18 = 90
1 men’s 1 day work = [1/18]
1 women’s 1 day work = [1/90]
Now,
4 men’s 1 day work = (4 × [1/18]) = [2/9]
10 women’s 1 day work = (10 × [1/90]) = [1/9]
Therefore, (4 men + 10 women)’s 1 day work =
2/9 + 1/9 à (2+1)/9 à 3/9 à 1/3
Therefore, 4 men and 10 women will complete the work in 3 days

SHORTCUT METHOD:
Now the work done by 3 men in 6 days and 5 women in 18 days is equal
Therefore, 3 men × 6 days = 5 women × 18 days
18 men = 90 women
1 man = 5 women
Substitute, the above in 4 men + 10 women = 4 men + 2 men = 6 men
No. of days taken by 4 men & 10 women = [18 men / 6 men] = 3 days

ALTERNATE METHOD:
This can also be solved by taking the number of women in consideration
4 men + 10 women = 20 women + 10 women as (1man = 5women)
= 30 women
Now no. of days taken by 4 men & 10 women = [90 women / 30 women] = 3 days

(357)

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