Question

Raju takes 6 days less than ramu to finish a pieceof work if both of them together can finish the work in 4 days in how many days Raju alone can finish the work ​

Answer 1

Answer:

I hope that you will be able to understand

Answer 2

AnSwer :

• Let the time taken by the ramu be M hours.
• And time taken by the Raju be (M - 6) years.
• Time taken by both ramu and raju together to complete the work is 4 days.

$\dag\:\underline{\textbf{According to the Question Now :}}$

$:\implies \sf \dfrac{1}{M} + \dfrac{1}{M - 6} = \dfrac{1}{4}$

$:\implies \sf \dfrac{M - 6 +M }{M(M - 6)} = \dfrac{1}{4}$

$:\implies \sf \dfrac{2M - 6 }{M ^{2} - 6M} = \dfrac{1}{4}$

$:\implies \sf 4(2M - 6)=1(M ^{2} - 6M)$

$:\implies \sf 8M - 24=M ^{2} - 6M$

$:\implies \sf M ^{2} - 6M - 8M + 24 = 0$

$:\implies \sf M ^{2} - 14M + 24 = 0$

$:\implies \sf M ^{2} - 12M - 2M+ 24 = 0$

$:\implies \sf M(M - 12) - 2(M - 12) = 0$

$:\implies \sf (M - 2)(M - 12) = 0$

$:\implies \underline{ \boxed{ \sf M = 12 \: or \: M = 2}}$

As M = 2 is not acceptable beacuse M - 6 = 2 - 6 = -4.

Hence,Raju alone can finish the work in 12 hours.