Question
A, B and C can together do a job in 9 days. C alone can do the job in 36 days. In how many days can A and B do 50% of the job working together ?
6
12
9
15

Solution
Correct option is 6

माना A तथा B काम को T दिन में करते हैं। (A+B+C) का 1 दिन का $= \dfrac 19$ प्रश्नानुसार, $\dfrac 1T + \dfrac 1 { 36 } = \dfrac 19 \\ \Rightarrow \dfrac 1T = \dfrac 19 - \dfrac 1 { 36 }$ $\Rightarrow T = 12$ दिन (A+B) द्वारा काम का 50% भाग पूरा करने में लगा समय $= 12 \times \dfrac{ 50 }{ 100 } = 6$दिन

Question
A can do 1/5 of a job in 10 days, B can do 1/3 rd of the job in 25 days. In how many days can they do half of the job working together ?
30
45
15
20

Solution
Correct option is 15

A और B पूरे कार्य को क्रमश: 50 दिनों तथा 7512 दिनों में कर सकते हैं। दोनों का 1 दिन का कार्य $= \dfrac{ 1 }{ 50 }+\dfrac{1}{ 7 5 }\\ = \dfrac{ 3+2 }{ 150 } = \dfrac 1 { 30 }$ अतः आधा हिस्सा पूरा करने में लगा समय = 15 दिन

Question
P and Q together can do a work in 12 days. P alone can do the same work in 36 days. In how many days can Q alone complete two-third part of the same work?
18
21
15
12

Solution
Correct option is 12

(P+Q) का एक दिन का काम = $\dfrac 1{ 12}$ P का एक दिन का काम = $\dfrac1{ 36 }$ Q का एक दिन का काम = $\dfrac { 1}{ 36 }= \dfrac 1 { 18}$ भाग $\because \dfrac{ 1 }{ 18 }$ भाग काम पूरा करने में Q को 1 दिन लगता है। $\because \dfrac 23$ भाग काम पूरा करने में Q को लगा समय $= 18 \times \dfrac23$ $= 12$ दिन

Question
Ramu works 4 times as fast as Somu. If Somu can complete a work in 20 days independently, then the number of days in which Ramu and Somu together can complete the work is:
3 days
5 days
4 days
6 days

Solution
Correct option is 4 days

रामू तथा सोमू के कार्य क्षमता का अनुपात = 4:1 कुल कार्य = 20 $\times$ 1 = 20 यूनिट अतः अभीष्ट समय = $\dfrac { 20} 5$ = 4 दिन

Question
X can do a work alone in 15 days Y can do the same work alone in 30 days. X, Y and Z work together and completes the same work in 9 days. In how many days Z can complete the same work alone?
120
90
45
60

Solution
Correct option is 90

#file_1633345794543 Z का एक दिन का काम = 10 - (6+3) = 1 यूनिट Z अकेला पूरे काम को करेगा = $\dfrac {90}1$ = 90 दिन

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