Question

The water level in a well was $20\mathrm{m}$ below ground level. During the rainy season, rain water collected in different water tanks was drained into the well and the water level rises $5\mathrm{m}$ above the previous level. The wall of the well is $1\mathrm{m}\mathrm{and}20\mathrm{cm}$ high and a pulley is fixed at a height of $80\mathrm{cm}$. Raghu wants to draw water from the well. The minimum length of the rope that he can use is,

• A. $17\mathrm{m}$
• B. $18\mathrm{m}$
• C. $96\mathrm{m}$
• D. $97\mathrm{m}$

Answer 1

The correct option is A

$17\mathrm{m}$

The explanation for the correct option.

It is given that the height of the wall of the well$=1\mathrm{m}20\mathrm{cm}=1.2\mathrm{m}$

and the height of the fixed pulley $=80\mathrm{cm}=0.8\mathrm{m}$

Initially, water was available at a depth of $20\mathrm{m}$ below ground level. Later, due to rain, the water level was raised by $5\mathrm{m}$.

Hence, the new depth at which water is available $=20–5=15\mathrm{m}$

Thus, the minimum length of the rope required to draw water from the well will be,

$1.2+0.8+15=17\mathrm{m}$

Hence, the option $A$ is correct.