Mugdha and Mayuri Working Together, Can Complete a Job In 18 Days Aptitude Question SOLUTION

Mugdha and Mayuri Working Together, Can Complete a Job In 18 Days.However, Mayuri works alone And Leaves after Completing Two-Fifth(2/5) of the job Than mugdha Takes Over And Complete The Remaining Work By herself,As a result They Could Complete The Job In 39 Days, How Mnay Days Would Mugdha Alone Have To Do The Job,If Mayuri Works Faster Than Mugdha?

Answer:-45 days




Full Solutions Is Below The Post


मुग्धा और मयूरी एक साथ काम करते हुए, 18 दिनों में एक काम पूरी कर सकते हैं। हालांकि, मयूरी अकेले काम करती है और काम के दो-पांचवीं (2/5) पूरा करते ही काम छोड़ देती है I
 और फिर मुग्धा काम करना शुरू कर देती है
और खुद से शेष कार्य को पूरा करती है,
 परिणामस्वरूप वे 39 दिनों में काम पूरी करते हैं,
मयूरी मुगाधा की तुलना में तेजी से काम करती है।
तो मुग्धा को अकले इस काम को करने में कितने दिनों का समय लगेगा?


Answer:-45 days

Solutions

If, Mugdha and Mayuri working together can complete a job in 18 days

After 1 day = 1/18 of the work Done


Let,
Mayuri's  Efficiency   = X
Mugdha's Efficiency  = Y

Mayuri take X days to complete the work alone
After 1 day = 1/X of the work Done By Mayuri

 &

Mugdha take Y days to complete the work alone

After 1 day = 1/Y of the work Done By Mugdha

So, Work Done = (1/X + 1/Y) = 1/18  --------------------(1)



If,Mayuri did 2/5 of the work and Mugdha did 3/5 of the work, they took 39 days.


2/5 x + 3/5 y = 39  --------------------(2)

than,

From (1)

(1/X + 1/Y) = 1/18 

(Y+X)/XY = 1/18

XY =18(Y+X)

18Y = XY-18X

18Y = X(Y-18)

So,
X = (18Y/Y-18)




A/Q,

From (2)

(2X/5) + (3Y/5) =39

2/5 (18y/(y - 18))  + 3y/5 = 39     -----------------   (Put The Value Of  X  in Eqn)

(36Y/5(Y-18)) + 3Y/5 = 39

36y + 3y(y - 18) = 39(5(y - 18))

36y + 3y² - 54y = 195y - 3510

3y² - 213y + 3510 = 0

y² - 71Y + 1170 = 0

(Y - 26) (Y - 45) = 0

Y = 26 or Y = 45


When y = 26

1/x + 1/y = 1/18

1/x + 1/26 = 1/18

1/x = 2/117

x = 117 ÷ 2 = 58.5 Which Is Not Possible
 Because  If Mayuri takes 58.5 days, Mugdha takes 26 days


When y = 45,

1/x + 1/y = 1/18

1/x + 1/45 = 1/18

1/x = 1/30

x = 30

If Mayuri takes 30 days, Mugdha takes 45 days








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