A garrison had provision for a certain number of days. After 10 days, $$\frac{1}{5}$$ of the men desert and it is found that the provisions will now last just as long as before. How long was that ?
A. 15 days
B. 25 days
C. 35 days
D. 50 days
Answer: Option D
Solution(By Examveda Team)
Initially, Let there be x men having food for y daysAfter 10 days, x men had food for days (y - 10)
Also, $$\left( {x - \frac{x}{5}} \right)$$ men had food for y days
$$\eqalign{ & \therefore \,x\left( {y - 10} \right) = \frac{{4x}}{5} \times y \cr & \Leftrightarrow 5xy - 50x = 4xy \cr & \Leftrightarrow xy - 50x = 0 \cr & \Leftrightarrow x\left( {y - 50} \right) = 0 \cr & \Leftrightarrow y - 50 = 0 \cr & \Leftrightarrow y = 50 \cr} $$
This Question Belongs to Arithmetic Ability >> Chain Rule
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Related Questions on Chain Rule
A. Rs. $$ {\frac{{{\text{xy}}}}{{\text{d}}}} $$
B. $${\text{Rs}}{\text{.}} {xd} $$
C. $${\text{Rs}}{\text{.}} {yd} $$
D. Rs. $$ {\frac{{{\text{yd}}}}{{\text{x}}}} $$
A. $$29\frac{1}{5}$$
B. $$37\frac{1}{4}$$
C. 42
D. 54
Let men=m day=d
ATQ
md=10m+4m/5 ×d we know that TW=D×E
=>5md=50m+4md
=>md=50m
=>d=50