Samir and Puneet can complete the same work in 10 days and 15 days respectively. The work was assigned for Rs.4500. After working together for 3 days Samir and Puneet involved Ashok. The work was completed in total 5 days. What amount (in Rs.) was paid to Ashok?

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SSC CGL 2020 Tier-I Official Paper 6 (Held On : 16 Aug 2021 Shift 3)
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  1. 1500
  2. 800
  3. 750
  4. 1071

Answer (Detailed Solution Below)

Option 3 : 750
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PYST 1:SSC CGL 2023 - Quantitative Aptitude(Held On:14 Jul 2023 Shift 1)
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25 Questions 50 Marks 20 Mins

Detailed Solution

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Given:

Samir's 1 day's work = 1/10

Puneet's 1 day's work = 1/15

Calculation:

(Samir + Puneet)'s 1 day's work = 1/10 + 1/15 = 1/6

(Samir + Puneet)'s 3 days work = 3 × 1/6 = 1/2

Remaining work after 3 days = 1 - 1/2 = 1/2

Remaining work completed in 2 days.

(Samir + Puneet + Ashok)'s 1 day's work = 1/2 × 1/2 = 1/4

Ashok's 1 day's work = 1/4 - 1/6 = 1/12

Ratio of work done = 5/10 : 5/15 : 2/12

= 1/2 : 1/3 : 1/6

= 3 : 2 : 1

∴ Ashok's share = 1/6 × 4500 = Rs.750

Alternate Method Samir and Puneet can complete the same work in 10 days and 15 days respectively

Total work = LCM(10, 15) = 30 units 

Efficiency of Samir = 30/10 = 3 units

Efficiency of Puneet = 30/15 = 2 units 

According to the question,

Samir and Puneet worked for (3 + 2) = 5 days 

Work done by Samir and Puneet in 5 days = 5 × 5 = 25 units 

Remaining 5 units of work is done by Ashok in 2 days

Efficiency of Ashok = 5/2 = 2.5 units 

Total amount = Rs. 4500

Amount given for 1 unit of work = 4500/30 = 150

Amount given to Ashok = 150 × 5 = Rs. 750

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