Question

43. A, B and C together can finish a work in 30 days. A and B take 9 days less to complete the same work than that of B and C.
C and A together can complete the work in 60 days. In how many days can A alone tinish the same work?
A, B और C मिलकर 30 दिनों में एक काम पूरा कर सकते हैं। A और B को मिलकर, B और C द्वारा एक साथ काम करने
की तुलना में समान कार्य पूरा करने में 9 दिन कम लगते हैं, C और Aमिलकर 60 दिनों में कार्य पूरा कर सकते हैं। A अकेले
कितने दिनों में काम पूरा कर सकता है?
a)120 days
b)72 days
c)90 days
d)144 days
​

Answer 1

A alone Finish the same work in 90 Days

Step-by-step explanation:

if A, B & C complete the work in A , B & C days alone respectively

then

A, B and C together can finish a work in 30 days

=> 1/A + 1/B  + 1/C  = 1/30

C and A together can complete the work in 60 days

=>  1/A +  1/C  = 1/60

=> 1/B = 1/30 - 1/60

=> 1/B = 1/60

=> B = 60

Let say B&C complete work in x Days

=> 1/B + 1/C  = 1/x

A and B take 9 days less to complete the same work

=> 1/B + 1/A  = 1/(x - 9)

Adding both

=> 1/B  +  (1/A + 1/B + 1/C)  = 1/x + 1/(x - 9)

=> 1/60 + 1/30  =  (2x - 9)/(x² - 9x)

=> 1/20 = (2x - 9)/(x² - 9x)

=> x² - 9x = 40x - 180

=> x² - 49x + 180 = 0

=> x² - 45x - 4x + 180 = 0

=> x(x - 45) - 4(x - 45) = 0

=> x = 4 or x = 45

x = 4 not possible

1/B + 1/A  = 1/(x - 9)

=> 1/60  + 1/A = 1/36

=> 1/A = 1/36 - 1/60

=> 1/A = (5 - 3)/180

=> 1/A = 2/180

=>  A = 90

A alone Finish the same work in 90 Days

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