A water-tank ‘T’ supplies 3000 litres of water. It supplies equal volume of water to the pipelines connecting the sub-stations P, Q & R. Similarly, sub-stations Q & R supply equal volume of water to the pipelines connecting them to their respective mini-stations. Sub-station P supplies water such that equal volume of water is received at mini-stations P1 & P2. The numbers indicate the length of the pipelines in km. It is observed that there is a loss of ‘x’% and ‘2x’% of water in the pipelines joining the tank to the sub-station and the pipelines joining the sub-stations to mini-stations respectively. (where ‘x’ represents the length of the pipeline).
Q1. How much water (in litres) is received at mini-station P1?
Q2. Find the length of pipe $\mathrm { Q } \rightarrow \mathrm { Q } _ { 3 }$ (in km.) if the sum of the volume of water received at $\mathrm { Q } _ { 1 }$ and $\mathrm { Q } _ { 3 }$ is 380 litres.
Q3. $\mathrm { L } _ { 1 }$ and $\mathrm { L } _ { 2 }$ are the lengths of $\mathrm { R } \rightarrow \mathrm { R } _ { 1 }$ and $\mathrm { R } \rightarrow \mathrm { R } _ { 2 }$ pipelines respectively. Also, it is known that $\mathrm { L } _ { 1 } + \mathrm { L } _ { 2 } = 25 \mathrm { km }$ . The sum of the volume of water received at mini-stations $\mathrm { R } _ { 1 }$ and $\mathrm { R } _ { 2 }$ is 600 litres. Find the length of the pipeline $\mathrm { T } \rightarrow \mathrm { R }$ .
- 10$\mathrm { km }$
- 30$\mathrm { km }$
- 25$\mathrm { km }$
- 20$\mathrm { km }$
Q4. Due to scarcity of water at sub-station Q, a new pipeline is fitted between sub-station R and sub-station Q. A water loss of 5x% is observed in the new pipeline where ‘x’ is the length of the pipeline (in km). Sub-station Q now supplies 300 litres of water in each pipeline to its mini-stations. Find the length of the new pipeline if R supplies equal volume of water to each pipeline. (Use data from the previous question if necessary)
- 12.5$\mathrm { km }$
- 11.25$\mathrm { km }$
- 17.5$\mathrm { km }$
- 8.75$\mathrm { km }$