Question

A & B can do a piece of work in 60 & 75
days respectively. Both begin together,
but after certain days A leaves off. In
such a case B finishes the remaining
work in 30days. After how many days
leaves off?​

Answer 1

Gɪᴠᴇɴ :-

• A & B can do a piece of work in 60 & 75
• days respectively.
• Both begin together, but after certain days A leaves off.
• In such a case B finishes the remaining work in 30days.

Tᴏ Fɪɴᴅ :-

• After how many days A leaves off ?

Sᴏʟᴜᴛɪᴏɴ :-

LCM of 60 & 75 = 300 unit = Let Total work.

So,

→ Efficiency of A = (Total work) / (Total No. of Days.) = (300/60) = 5 units/day.

Similarly,

→ Efficiency of B = (Total work) / (Total No. of Days.) = (300/75) = 4 units/day.

Now, we have given that, Both begin together,

Both begin together,but after certain days A leaves off and, B finishes the remaining work in 30days.

So,

→ in Last 30 days B alone did = 30 * 4 = 120 units of work.

Therefore, we can say that, rest amount of work was done by both (A + B) before A left.

So,

→ Left work = 300 - 120 = 180 units

And,

→ Time taken by (A + B) Now = (Left work) / (Efficiency of Both) = 180 / (5 + 4) = 180/ 9 = 20 days. (Ans.)

Hence, A leaves off after 20 days.

Answer 2

${ \tt{ \underline{ \huge {\purple{Question}}}}}$




▪ A and B can do a piece of work in 60 and 75 days respectively. Both begin together but after certain days A leaves off . In such a case B finishes the remaining work in 30 days. After how many days A leaves off?



${ \tt{ \underline{ \purple{ \huge{Solution}}}}}$




${ \star{ \red{ \sf{ \: A \: can \: do \: a \: piece \: of \: work \: in \: 60 \: days}}}}$




${ \star{ \sf{ \red{ \: B \: can \: do \: the \: same \: work \: in \: 75 \: days}}}}$



then, let the total work be the L.C.M. of 60 and 75 i.e.,




${ \rightarrow{ \blue{ \sf{total \: work = 300 \: units}}}}$




NOW,



${ \tt{the \: \: working \: \: efficiency \: \: of - }}$



${ \star{ \sf{ \orange{ \: \: A= \frac{total \: work}{time \: taken \: by \: A }}}} }$




$= { \orange{ \sf{ \frac{300 \: unit}{60 \: day}}} \: = { \red{ \sf{5 \frac{unit}{day}}}} }$




${ \star{ \sf{ \orange{ \: \: \: B = \frac{total \: work}{time \: taken \: by \: B}}}}}$




$= { \sf{ \orange{ \frac{300 \: unit}{75 \: day}} = { \sf{ \red{4 \frac{units}{day}}}}}}$




▪ It's given in the question that both, A and B started the work together , but after certain days A leaves off



and B finishes the remaining work in 30 days



➡ that means B worked alone for the last 30 days



${ \sf{ \pink{amount \: of \: work \: done \: by \: B }}} \\ { \sf{ \pink{ \: in \: last \: 30 \: days}}} \: = { \sf{ \blue{4 \frac{ units}{day} \times 30 \: day}}}$




$= { \blue{ \sf{120 \: units}}}$




Then, it can be said that the remaining amount of work was done by (A+B) together , before A left.....



${ \sf{ \pink{work \: done \: by \: (A + B) \: together }}} \\ = { \sf{ \blue{total \: work - work \: done \: by \: B \: alone}}}$




$= { \sf{ \blue{300 \: units - 120 \: units}}}$



$= { \blue{ \sf{180 \: units}}}$



Then,




${ \red{ \sf{time \: taken \: by \: (A + B) }}} \\ = { \sf{ \blue{ \frac{work \: done \: by \: (A + B)}{efficiency \: of \: (A + B)}}}}$




$= { \sf{ \blue{ \frac{180 \: units}{(5 + 4) \frac{units}{day}}}} } = { \sf{ \blue{ \frac{180 \: day}{9}}}}$




▪ therefore,



${ \star{ \sf{ \purple{ \: \: time \: taken \: by \: (A + B) = 20 \: days}}}}$




thus,



${ \underline{ \boxed{ \orange{ \sf{A \: left \: after \: 20 \: days}}}}}$