Question

40. Working alone, A can complete a work by the end of the 14th day of a month while B, working alone, can complete the work by the end of the 18th day of the month, had they started on the beginning of the pth day of the month. A started working on the beginning of the pth day of the month and worked till the end of the 12th day of the month, handing over the remaining work to B. If the work was completed by the end of the 15th day of the month, find p. (A) 7th day (B) gth day (C) 9th day (D) 6th day​

Answer 1

Answer:

pak ki or badh raha to you bhai u

Step-by-step explanation:

Happy the information contained within this question on class kal PDP

Answer 2

Given :- When they started on the beginning of the pth day of the month :- , A can complete a work by the end of the 14th day of a month while B, working alone, can complete the work by the end of the 18th day of the month .

Also, A started working on the beginning of the pth day of the month and worked till the end of the 12th day of the month, handing over the remaining work to B. The work was completed by the end of the 15th day of the month .

To Find :- Value of p :-

(A) 7th day (B) 8th day (C) 9th day (D) 6th day .

Solution :-

Case 1) :-

→ Time taken by A alone to complete total work = from beginning of pth day to the end of 14th day = (14 - p) + 1 = (15 - p) days .

So,

→ Per day work of A = 1/(15 - p) unit

similarly,

→ Time taken by B alone to complete total work = from beginning of pth day to the end of 18th day = (18 - p) + 1 = (19 - p) days .

So,

→ Per day work of B = 1/(19 - p) unit

Case 2) :-

→ Number of days A worked alone = from beginning of the pth day till the end of the 12th day = (12 - p) + 1 = (13 - p) days .

So,

→ Work done by A alone in (13 - p) days = Per day work × Total days = 1/(15 - p) × (13 - p) = {(13 - p)/(15 - p)} units .

now,

→ Number of days B worked alone = from beginning of the 13th day till the end of the 15th day = (15 - 13) + 1 = 3 days .

So,

→ Work done by B alone in 3 days = Per day work × Total days = 1/(19 - p) × 3 = {3/(19 - p)} units .

A/q,

→ Work done by A alone + Work done by B alone = 1

→ {(13 - p)/(15 - p)} + {3/(19 - p)} = 1

→ (13 - p)(19 - p) + 3(15 - p) = (15 - p)(19 - p)

→ 247 - 13p - 19p + p² + 45 - 3p = 285 - 15p - 19p + p²

→ 292 - 35p + p² = 285 - 34p + p²

→ 292 - 35p = 285 - 34p

→ 35p - 34p = 292 - 285

→ p = 7th day (Ans.)

Hence, Value of p is equal to Option (A) 7th day of the the month .

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