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A takes 12 days less than the time taken by B to finish a piece of work. If both A and B can do it in 8 days, then the time taken by B alone to finish the work is
- A24 days
- B28 days
- C20 days
- D16 days
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CCommunity
Given, A takes 12 days less than the time taken by B to finish a piece of work.
Let the number of days in which B finishes the work be ‘a’ days
Number of days in which A finishes the work = a – 12 days
Now, both A and B can do it in 8 days.
$(\Rightarrow \frac{1}{a} + \frac{1}{{a - 12}} = \frac{1}{8})$
⇒ (a + a -12) × 8 = a2 – 12a
⇒ a2 – 28a + 96 = 0
⇒ a2 – 24a - 4a + 96 = 0
⇒ a(a – 24) – 4(a – 24) = 0
⇒ (a – 4)(a – 24) = 0
⇒ a can’t be 4 thus a = 24 days
Let the number of days in which B finishes the work be ‘a’ days
Number of days in which A finishes the work = a – 12 days
Now, both A and B can do it in 8 days.
$(\Rightarrow \frac{1}{a} + \frac{1}{{a - 12}} = \frac{1}{8})$
⇒ (a + a -12) × 8 = a2 – 12a
⇒ a2 – 28a + 96 = 0
⇒ a2 – 24a - 4a + 96 = 0
⇒ a(a – 24) – 4(a – 24) = 0
⇒ (a – 4)(a – 24) = 0
⇒ a can’t be 4 thus a = 24 days