1. X is 3 times as fast as Y and is able to complete the work in 40 days less than Y. Then the time in which they can complete the work together is
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By: anil on 05 May 2019 02.00 am
Let the number of days taken by Y to complete the work be "a".
Since X is three times as fast as Y Work completed per day by X is given by
$$frac{1}{X} = frac{3}{Y}$$
$$a frac{1}{Y} =1$$ -------------- 1
Since X takes 40 days less time than Y
$$(a-40) frac{1}{X} =1$$ ----------------- 2
Replacing $$frac{1}{X}$$ in 2 and solving for "a" we get
a=60 days.
Substituting a in 1 and 2 we get
$$frac{1}{X} = frac{1}{20}$$
$$frac{1}{Y} $$$$= frac{1}{60}$$
Let the number of days it takes when both X and Y are working together be $$n$$.
$$ n imes ( frac{1}{X} + frac{1}{Y}) =1 $$
$$ n imes ( frac{1}{20} + frac{1}{60}) =1 $$
$$n=15$$
Hence Option A is the correct answer.
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Since X is three times as fast as Y Work completed per day by X is given by
$$frac{1}{X} = frac{3}{Y}$$
$$a frac{1}{Y} =1$$ -------------- 1
Since X takes 40 days less time than Y
$$(a-40) frac{1}{X} =1$$ ----------------- 2
Replacing $$frac{1}{X}$$ in 2 and solving for "a" we get
a=60 days.
Substituting a in 1 and 2 we get
$$frac{1}{X} = frac{1}{20}$$
$$frac{1}{Y} $$$$= frac{1}{60}$$
Let the number of days it takes when both X and Y are working together be $$n$$.
$$ n imes ( frac{1}{X} + frac{1}{Y}) =1 $$
$$ n imes ( frac{1}{20} + frac{1}{60}) =1 $$
$$n=15$$
Hence Option A is the correct answer.