The history of renewable energy suggests there is a steep learning curve, meaning that, as more is produced, costs fall rapidly because of economies of scale and learning by doing. The firms' green innovation is path-dependent: the more a firm does, the more it is likely to do in the future. The strongest evidence for this is the collapse in the price of solar energy, which became about $90 \%$ cheaper during the 2010s, repeatedly beating forecasts. Moving early and gradually gives economies more time to adjust, allowing them to reap the benefits of pathdependent green investment without much disruption. A late, more chaotic transition is costlier.

Team $X$ scored a total of $N$ runs in 20 overs. Team $Y$ tied the score in $10 \%$ less overs. Had team Y's average run rate (runs per over) been $50 \%$ higher, the scores would have been tied in 12 overs. How many runs were scored by team X?

The history of renewable energy suggests there is a steep learning curve, meaning that, as more is produced, costs fall rapidly because of economies of scale and learning by doing. The firms' green innovation is path-dependent: the more a firm does, the more it is likely to do in the future. The strongest evidence for this is the collapse in the price of solar energy, which became about $90 \%$ cheaper during the 2010s, repeatedly beating forecasts. Moving early and gradually gives economies more time to adjust, allowing them to reap the benefits of pathdependent green investment without much disruption. A late, more chaotic transition is costlier.

The price (p) of a commodity is first increased by $\mathbf{k} \boldsymbol{\%}$; then decreased by $\mathrm{k} \%$; again increased by $\mathrm{k} \%$; and again decreased by $\mathrm{k} \%$. If the new price is q , then what is the relation between $p$ and $q$ ?

If the social inequality is the most acutely felt social problem in India, insecurity, more than poverty, is the most acutely felt economic problem. Besides those below the official poverty line, even those just over the poverty line are subject to multiple economic insecurities of various kinds (due to wealth and/or health risks, market fluctuations, job-related uncertainties). Many Government policies are actually intended towards mitigating these insecurities.

The petrol price shot up by $10 \%$ as a result of the hike in crude oil prices. The price of petrol before the hike was ₹$ 90$ per litre. A person travels 2200 km every month and his car gives a mileage of 16 km per litre. By how many km. should he reduce his travel if he wants to maintain his expenditure at the previous level?

If there is inequality in the pattern of population growth, there is greater inequality in food production and utilisation. As societies become wealthier, their consumption of animal products increases. This means that a greater proportion of such basic foodstuff as grains and legumes that could feed humans directly is instead being converted into feed for poultry and large farm animals. Yet this conversion of plant-based food into animal food for humans is far from efficient. Only $16 \%$ of the calories fed to chickens are recovered by us when we eat them. This conversion rate goes down to five to seven per cent in large animals that are fed grain to add fat and some protein before slaughter.

$P$ and $Q$ walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. $P$ walks at an average speed of 5 rounds per hour and Q walks at an average speed of 3 rounds per hour. How many times will they cross each other between 5:20 a.m. and 7:00 a.m.?