A started a work and left working after 9 days now B finished the remaining work in 24 days. Had A left the work after working for 13 days then B would have finished the remaining work in next 18 days. Then find in how many days A and B together can complete the work

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MP Vyapam Group 4 (Assistant Grade-3/Stenographer) Official Paper (Held On: 16 July, 2023 Shift 1)
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  1. 12 days 
  2. 15 days 
  3. 16 days
  4. 18 days 

Answer (Detailed Solution Below)

Option 2 : 15 days 
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MP व्यापम ग्रुप 4 सामान्य हिंदी सब्जेक्ट टेस्ट 1
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Detailed Solution

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Given:

A worked for 9 days, B finished the remaining work in 24 days.

A worked for 13 days, B finished the remaining work in 18 days.

Formula used:

Work = Rate × Time

Calculation:

Let 'a' be the fraction of work A does in one day, and 'b' be the fraction of work B does in one day.

From the given information:

 9a + 24b = 1 (whole work) ---- (1)

And, 13a + 18b = 1 (whole work) -- (2)

Multiply Equation 1 by 13 and Equation 2 by 9:

117a + 312b = 13

117a + 162b = 9

Subtract the second equation from the first:

150b = 4

b = 4/150 = 2/75

Substitute b = 2/75 into Equation 1:

9a + 24(2/75) = 1

9a = 1 - 48/75

9a = 27/75

a = 3/75 = 1/25

A's rate of work is 1/25 of the work per day.

B's rate of work is 2/75 of the work per day.

Combined rate of A and B

⇒ a + b = 1/25 + 2/75 = 3/75 + 2/75 = 5/75 = 1/15

If A and B work together, they complete 1/15 of the work in one day.

Let 'd' be the number of days A and B take together to complete the work.

(1/15) × d = 1

d = 15

∴ A and B together can complete the work in 15 days.

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