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PUNIT SHARMA

· started a discussion

· 1 Months ago

61 (Question:959709.0)

any short trick

Question:

Three cooks have to make 80 idlis. They are known to make 20 pieces every minute working together. The first cook began working alone and made 20 pieces having worked for some time more than three minutes. The remaining part of the work was done by the second and the third cook working together. It took a total of 8 minutes to complete the 80 idlis. How many minutes would it take the first cook alone to cook 160 idlis for a marriage party the next day? 

Options:
A)

    16 minutes

B)

    24 minutes 

C)

    32 minutes

D)

    40 minutes

Solution:

Ans:(c)

Let A be the number of idlis cooked by first cook per min. Similarly B and C for  second and third cook.

 Time required to cook 160 idlis by first cook be T 

  ∴     A=160T   

    Time required for 20 idlis =    ________(i)

    

  ∴       A + B + C = 20

  ⟹     160T+48064–T=20   

  ∴     8T+2464–T=1   

  ⟹    64T – T2 = 512 – 8T + 24T

  ⟹    T2 – 48T + 512=0

    On solving we get 

        T = 16, 32

    Given  T8>3    (Given 8 Idlis in more than 3 minutes)

  ⟹    T > 24

    So, T = 32


Alternative solution

let the rates be x,y,z
we know x+y+z = 20 and 20x+60y+z=8
putting (y+z) = (20-x) we get

x2−15x+50=0
solving we get x= 5,10; x cannot be 10 because 20x>3

so to prepare 160 burgers, time reqd. = \(\frac{160}{5}\)  = 32

Knowledge Expert

· commented

· 1 Months ago

Dear student,
We have updated the alternative or shortcut solution .Please check now, keep learning with us.

Regards
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