Question

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



​

Answer 1

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.].

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

Answer 2

Step-by-step explanation:

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{gathered}\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}\end{gathered}

\cline1−2x

\cline1−2Number of men

\cline1−2540

\cline1−2540+60

\cline1−2

y

Number of days

160

?

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\:menx

1

=540men

\sf x_{2} = 540 + 60\:menx

2

=540+60men

\sf y_{1} = 160\:daysy

1

=160days

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

2

=

x

2

x

1

×y

1

By substituting the values, we get :

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

2

=

540+60

540×160

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

2

=

600

540×160

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

2

=

6



0



0

54



0×16



0

\implies \sf y_{2} = 9 \times 16⟹y

2

=9×16

\implies \sf y_{2} = 144⟹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}}⟶

x

2

x

1

=

y

1

y

2