A tank is initially filled with $\frac{5}{8}$ of its capacity with oil. Due to a leak, $\frac{1}{5}$ of the oil in the tank is wasted during a day. (i) What fraction of the whole tank was empty at the beginning? (ii) What fraction of the oil in the whole tank got wasted during a day? (iii) At the end of the day, if 100 liters of oil was remaining in the tank, what is the capacity of the tank? (iv) If one liter of oil costs Rs. 450, find the value of the oil that got wasted.

1. Problem Description

A tank is initially filled with $\frac{5}{8}$ of its capacity with oil. Due to a leak, $\frac{1}{5}$ of the oil in the tank is wasted during a day.

(i) What fraction of the whole tank was empty at the beginning?

(ii) What fraction of the oil in the whole tank got wasted during a day?

(iii) At the end of the day, if 100 liters of oil was remaining in the tank, what is the capacity of the tank?

(iv) If one liter of oil costs Rs. 450, find the value of the oil that got wasted.

2. Solution Steps

(i) Fraction of tank empty at beginning:

Since the tank is $\frac{5}{8}$ filled, the empty portion is $1 - \frac{5}{8}$.

$1 - \frac{5}{8} = \frac{8}{8} - \frac{5}{8} = \frac{3}{8}$

(ii) Fraction of oil wasted during the day:

The fraction of oil wasted is $\frac{1}{5}$ of the $\frac{5}{8}$ of the tank's capacity that was initially filled.

Fraction of oil wasted = $\frac{1}{5} \times \frac{5}{8} = \frac{1 \times 5}{5 \times 8} = \frac{5}{40} = \frac{1}{8}$

(iii) Capacity of the tank:

Let the capacity of the tank be $x$ liters.

Initially, the tank had $\frac{5}{8}x$ liters of oil.

Oil wasted = $\frac{1}{8}x$ liters

Remaining oil = Initial oil - Wasted oil

$100 = \frac{5}{8}x - \frac{1}{8}x = \frac{4}{8}x = \frac{1}{2}x$

$100 = \frac{1}{2}x$

$x = 2 \times 100 = 200$

So, the capacity of the tank is 200 liters.

(iv) Value of the oil that got wasted:

The amount of oil wasted is $\frac{1}{8}$ of the tank's capacity, which is $\frac{1}{8} \times 200 = 25$ liters.

Cost of 1 liter of oil = Rs. 450

Cost of 25 liters of oil = $25 \times 450 = 11250$

3. Final Answer

(i) $\frac{3}{8}$

(ii) $\frac{1}{8}$

(iii) 200 liters

(iv) Rs. 11250