Question

Two persons a and b can do a work alone in 29 days. A takes the rest of one day after every 4 days and b takes the rest of one day after every 5 days. If a and b starts working together, then the work will be completed on [1] 15th day [2] 16th day [3] 17th day [4] 18th day

Answer 1

Answer:

Step-by-step explanation:

Since a and b can do a work alone in 29 days

so one day work of A = 1/29

     one day work of B = 1/29

     means A and B both do 1 unit of work in one day individually

A and B do work together 4 days so

work  done by both in after 4 days = 2*4 = 8

after 4 days A and B do work alternatively for 2 days so 2 days work = 2 unit

work done after 6 days = 8 + 2 = 10 unit

so after 12 days work = 20 unit

After 16 days work done = 20+ 2*4

                                         = 28 unit

At last day i.e. 17 day B will do 1 unit so

work done =  29 unit

Hence work will be completed on 17th day

Answer 2

Concept:

Profit and loss statements are calculated by subtracting a company's total revenue from its total expenses, including taxes. The resulting figure is referred to as net income. If it is negative, the company has lost money; if it is positive, the company has made money.

Given: Two persons a and b can do a work alone in $29$ days. A takes the rest of one day after every $4$ days and b takes the rest of one day after every $5$ days. If a and b starts working together.

Find: If a and b starts working together, then the work will be completed on [1] 15th day [2] 16th day [3] 17th day [4] 18th day.

Solution:

A and B have same performance of work i.e.$1/29$

they start to gather till forth day and A takes rest fifth day B takes rest and so on for next cycle…..

work done in$5$ days by both is $4*2/29+1/29 = 9/29$

there will be $3$ such cycle i.e. $3*5=15$days (i.e. $9/29*3 = 27/29$ of job completed

left over job at start of $16 th$ day $1$–$27/29= 2/29$

$2$ day more to be carried first by b then he takes rest

completed by a in last day

total days $17$.

Hence the correct is [3] 17th day.

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