A drum of kerosene oil is 3/4 full. When 15 litres of oil is drawn from it, it is 7/12 full.Find the total capacity of the drum ?

Question

Ethan Adkins · Accepted Answer

90 litres.

Let the total capacity be #x#. According to the question, #(3x/4)-15=(7x/12)# #(3x-60)/4=(7x/12)# #3x-60(12)=(7x)×4# #36x-720=28x# #36x-28x=720# #8x=720# #x=90#

Isaiah Anthony · Answer

undefined To find the total capacity of the drum, we can set up the equation:

(3/4)x - 15 = (7/12)x

Solving for x:

(3/4)x - (7/12)x = 15
(9/12)x - (7/12)x = 15
(2/12)x = 15
x = 15 * (12/2)
x = 90

So, the total capacity of the drum is 90 litres.

HIX Tutor · Answer

undefined Let's think about the problem together!

1. **Start with the amount of oil before drawing any out.**
   The drum is initially $ \frac{3}{4} $ full.

2. **Next, when 15 liters of oil is taken out, the drum is $ \frac{7}{12} $ full.** 
   What does this mean? It means we need to find the amount of oil left after taking out 15 liters.

3. **Let’s express the full capacity of the drum as $ C $ liters.**

4. **When the drum is $ \frac{3}{4} $ full, the amount of oil is:**
   $$
   \text{Amount when } \frac{3}{4} \text{ full} = \frac{3}{4}C
   $$

5. **After taking out 15 liters, it is $ \frac{7}{12} $ full, so the amount of oil now is:**
   $$
   \text{Amount when } \frac{7}{12} \text{ full} = \frac{7}{12}C
   $$

6. **We can now set up an equation:**
   $$
   \frac{3}{4}C - 15 = \frac{7}{12}C
   $$

7. **Let’s get the fractions to be the same. The common denominator is 12.**  
   - Convert $ \frac{3}{4} $ to twelfths:
   $$
   \frac{3}{4} = \frac{9}{12}
   $$
  
8. **Now we rewrite the equation:**
   $$
   \frac{9}{12}C - 15 = \frac{7}{12}C
   $$

9. **Subtract $ \frac{7}{12}C $ from both sides:**
   $$
   \frac{9}{12}C - \frac{7}{12}C = 15
   $$
   $$
   \frac{2}{12}C = 15
   $$

10. **Simplify $ \frac{2}{12} $ to $ \frac{1}{6} $:**
    $$
    \frac{1}{6}C = 15
    $$

11. **Now, multiply both sides by 6 to find $ C $:**
    $$
    C = 15 \times 6
    $$
    $$
    C = 90
    $$

So, what do you think is the total capacity of the drum?