SSC CGL Tier II 12 Apr 2015 Paper

Question : 59 of 100

Marks: +1, -0

Two workers A and B are engaged to do a piece of work. A working alone would take 8 hours more to complete the work than when work together. If B worked alone, would take

4 1 /2

hours more than when work together. The time required to finish the work together is

5 hours
4 hours
8 hours
6 hours

Validate

Solution:

(4) Time taken by A and B = x hours (let).
∴ According to the question,
Time taken by A alone = (x + 8) hours.
Time taken by B alone

= (x+ {9}/{2} )

hours.

∴{1}/{x+8}+ {1}/{x+ {9}/{2}}= {1}/{x}

⇒{1}/{x+8}+ {2}/{2 x+9}= {1}/{x}

⇒{2 x+9+2 x+16}/{(x+8)(2 x+9)}= {1}/{x}

⇒{4 x+25}/{2 x^{2}+16 x+9 x+72}= {1}/{x}

⇒4 x^{2}+25 x=2 x^{2}+25 x+72

⇒2 x^{2}=72 ⇒ x^{2}= {72}/{2}=36

⇒ x=√{36}=6

hours

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