A can do a piece of work in 120 days and B can do it in 150 days. They work together for 20 days. Then B leaves and A continues the work alone. 12 days after C joins A and the work is completed in 48 days more. In lion many days can C do it if he works alone?

Created: 3 months ago | Updated: 3 months ago

Job Solution Joint Recruitment Test Joint Recruitment Test for 3 Banks || Senior Officer (17-08-2018) || 2018 গণিত

প্রশ্নে বলা হচ্ছে যে, A একটি কাজ 120 দিনে এবং B কাজটি 150 দিনে করতে পারে। A এবং B একত্রে কাজটি 20 দিন করে B কাজটি ছেড়ে চলে গেল এবং A কাজটি চালিয়ে গেল। 12 দিন পরে C এসে A এর সাথে যোগ দিলে কাজটি শেষ করতে আরো 48 দিন সময় লাগল । C একা কাজটি কত দিনে করতে পারবে?

$A & B c a n d o i n 1 d a y = (\frac{1}{120} + \frac{1}{150}) = (\frac{5 + 4}{600}) = \frac{9}{600} = \frac{3}{200} P a r t o f t h e w o r k ∴ A & B c a n d o i n 20 d a y s = (\frac{3}{200} \times 20) = \frac{3}{10} P a r t o f t h e w o r k R e m a i n i n g w o r k = 1 - \frac{3}{10} = \frac{10 - 3}{10} = - \frac{7}{10} P a r t o f t h e w o r k$

$I n 12 d a y s, A c a n c o m p l e t e = \frac{1}{120} \times 12 = \frac{1}{10} P a r t o f t h e w o r k ∴ R e m a i n i n g w o r k = (\frac{7}{10} - \frac{1}{10}) = \frac{7 - 1}{10} = \frac{6}{10} = \frac{3}{5} P a r t o f t h e w o r k$

Let, C can do the work is x days

So, A & C can do in 1 day $= (\frac{1}{20} + \frac{1}{x}) = \frac{x + 120}{120 x} P a r t o f t h e w o r k$

$∴ A & C c a n d o i n 48 d a y s = \frac{48 (x + 120)}{120 x} P a r t o f t h e w o r k A c c o r d i n g t o q u e s t i o n, \frac{48 (x + 120)}{120 x} = \frac{3}{5} \Rightarrow 5 \times 48 (x + 120) = 360 x \Rightarrow 240 x + 28, 800 = 360 x \Rightarrow 360 x - 240 x = 28, 800 \Rightarrow 120 x = 28, 800 ∴ x = \frac{28800}{120} = 240 ∴ C c a n d o t h e w o r k 240 d a y s .$

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60 men could complete a piece of work in 250 days. They worked together for 200 days. After that the work had to be stopped for 10 day to bad weather. How many more men should be engaged to complete the work in time?

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