Question

6 men and 8 boys can do a piece of work in 7 days while 8 men and 12 boys can do the same work jin 5 days. How long would it take one boy to finish the same piece of work? (with solution)​

Answer 1

Answer:

Suppose 1 man alone can finish the work in x days and 1 boy alone can finish it in y days.

Then , 1 man's 1 day's work = 1x.

And, 1 boy's 1 day's work = 1y

8 men and 12 boys can finish the work in 5 days

⇒ ( 8 men's 1 day's work ) + ( 12 boy's 1 day's work ) =15

⇒8x+12y=15

⇒8u+12v=15  ... (i), where 1x=uand1y=v

Again, 6 men and 8 boys can finish the work in 7 days

⇒( 6 men's 1 day's work) + ( 8 boy's 1 day's work) =17

⇒6x+8y=17

⇒6u+8v=17 ... (ii)

On multiplying (i) by 3, (ii) by 4 and subtracting the results, we get

4v=(35−47)=135⇒v=1140⇒1y=1140⇒y=140

On putting v=1140 in (ii), we get

6u=(17−8140)=12140⇒u=(12140×16)=170

⇒1x=170⇒x=70

∴ one man along can finish the work in 70 days,

and one boy alone can finish the work in 140 days.

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