1.

. There is 160 days ration for 540 persons in a fort. After 10 days, 60 more personsjoin them. For how many days will theration sufficient at the same rate?​

Answer»

Given :-

  • Number of days RATION can last = 160 days
  • Number of PERSONS = 540
  • After 10 days, 60 more persons jöin.

Aim :-

  • To find the number of days the food will last if 60 more persons are included.

Answer :-

Let us tabulate the given hints.

\begin{array}{|c|c|}\cline{1-2} \bf x & \bf y \\\cline{1-2}\bf Number\ of\ men & \bf Number\ of\ days \\\cline{1-2} \bf 540 & \bf 160 \\\cline{1-2}\bf 540+60 & \bf ?\\\cline{1-2}\end{array}

if x ↑ then y ↓ and vice versa.

⇒ If the Number of men increases, the Number of days the ration lasts decreases.

Hence, x and y are in inverse proportion.

Let us assume the number of days the food will last when 60 more persons JOIN as y₂

  • \sf x_{1} = 540\:men
  • \sf x_{2} = 540 + 60\:men
  • \sf y_{1} = 160\:days

\implies \sf y_{2} = \dfrac{x_{1} \times y_{1}}{x_{2}}

By substituting the values, we get :

\implies \sf y_{2} = \dfrac{540 \times 160}{540 + 60}

\implies \sf y_{2} = \dfrac{540 \times 160 }{600}

\implies \sf y_{2} = \dfrac{54\not0 \times 16\not0}{6\not0\not0}

\implies \sf y_{2} = 9 \times 16

\implies \sf y_{2} = 144

Therefore, the food will last for 144 days, if 60 more people join the fort.

[x implies the number of men and y implies the number of days.].

  • \longrightarrow \sf \dfrac{x_{1}}{x_{2}} = \dfrac{y_{2}}{y_{1}}


Discussion

No Comment Found

Related InterviewSolutions