Determining the Total Weight of 10 Poles

The question asks us to find the total weight of 10 poles, given that all poles have the same weight. We need to assess if the provided statements are sufficient to find this total weight.

Analysis of Statement I

Statement I says: "One fourth of the weight of a pole is 5Kg".

Let the weight of a single pole be represented by the variable $w$. According to Statement I:

• $ \frac{1}{4} \times w = 5 $ Kg

To find the weight of one pole ($w$), we can rearrange the equation:

• $ w = 5 \text{ Kg} \times 4 $
• $ w = 20 $ Kg

Since we know the weight of one pole is 20 Kg, we can calculate the total weight of 10 poles:

• Total Weight = $ 10 \times w $
• Total Weight = $ 10 \times 20 $ Kg
• Total Weight = $ 200 $ Kg

Therefore, Statement I alone is sufficient to determine the total weight of the 10 poles.

Analysis of Statement II

Statement II says: "The total weight of these poles is 160kg more than the total weight of two poles."

Let the weight of one pole be $w$. The total weight of 10 poles is $10w$. The total weight of two poles is $2w$.

According to Statement II, the relationship is:

• Total Weight of 10 poles = Total Weight of 2 poles + 160 Kg
• $ 10w = 2w + 160 $ Kg

Now, we can solve this equation for $w$:

• $ 10w - 2w = 160 $ Kg
• $ 8w = 160 $ Kg
• $ w = \frac{160}{8} $ Kg
• $ w = 20 $ Kg

Again, knowing the weight of one pole is 20 Kg, we can find the total weight of 10 poles:

• Total Weight = $ 10 \times w $
• Total Weight = $ 10 \times 20 $ Kg
• Total Weight = $ 200 $ Kg

Therefore, Statement II alone is also sufficient to determine the total weight of the 10 poles.

Conclusion on Sufficiency

Since both Statement I and Statement II independently provide enough information to calculate the total weight of the 10 poles, we can conclude that either statement alone is sufficient.