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# Either of the team of A and B or team of C and D can do the a work in

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CAT Forum Moderator
Joined: 29 Nov 2018
Posts: 280
Concentration: Marketing, Strategy
Either of the team of A and B or team of C and D can do the a work in  [#permalink]

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06 Aug 2019, 03:37
00:00

Difficulty:

45% (medium)

Question Stats:

63% (03:11) correct 38% (03:32) wrong based on 8 sessions

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Either of the team of A and B or team of C and D can do the a work in 15 days. Also the same work can be done by the team of A and D in 10 days and by the team of B and C in 30 days. If B alone takes 40 days to complete the work, find the ratio of the number of days taken by the team of B and D and that taken by the team of A and C to complete the work.

1. 1 : 1
2. 3 : 5
3. 3 : 4
4. 1 : 2
5. Cannot be determined
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Joined: 25 Jul 2018
Posts: 712
Either of the team of A and B or team of C and D can do the a work in  [#permalink]

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06 Aug 2019, 04:59
2
$$\frac{1}{A}$$+$$\frac{1}{B}$$=$$\frac{1}{15}$$

$$\frac{1}{C}$$+$$\frac{1}{D}$$=$$\frac{1}{15}$$

--> $$\frac{1}{A}$$+$$\frac{1}{D}$$=$$\frac{1}{10}$$

--> $$\frac{1}{B}$$+$$\frac{1}{C}$$=$$\frac{1}{30}$$

$$\frac{1}{B}$$=$$\frac{1}{40}$$

--> ($$\frac{1}{B}$$+$$\frac{1}{D}$$)=$$\frac{1}{x}$$

--> ($$\frac{1}{A}$$+$$\frac{1}{C}$$)=$$\frac{1}{y}$$
-----------------
$$\frac{x}{y}$$=?

$$\frac{1}{C}$$=$$\frac{1}{30}$$-$$\frac{1}{40}$$=$$\frac{1}{120}$$

$$\frac{1}{D}$$=$$\frac{1}{15}$$-$$\frac{1}{120}$$=$$\frac{7}{120}$$

$$\frac{1}{A}$$=$$\frac{1}{15}$$-$$\frac{1}{40}$$=$$\frac{(8-3)}{120}$$=$$\frac{5}{120}$$

$$\frac{1}{B}$$+$$\frac{1}{D}$$=$$\frac{1}{40}$$+$$\frac{7}{120}$$=$$\frac{10}{120}$$=$$\frac{1}{12}$$=$$\frac{1}{x}$$ --> x=12

$$\frac{1}{A}$$+$$\frac{1}{C}$$=$$\frac{5}{120}$$+$$\frac{1}{120}$$=$$\frac{6}{120}$$=$$\frac{1}{20}$$=$$\frac{1}{y}$$--> y=20

--> $$\frac{x}{y}$$=$$\frac{12}{20}$$=$$\frac{3}{5}$$

Either of the team of A and B or team of C and D can do the a work in   [#permalink] 06 Aug 2019, 04:59

# Either of the team of A and B or team of C and D can do the a work in

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