For Devinder and Rehka Kumar, two was enough. After the birth of their second child – a boy – they realised they could not afford any more. The fact that they would receive a cash payment and even be given the chance to win a shiny new car if they actually did something about it only cemented their decision.

So last week, the 24-year-old Ms Kumar found herself among a small group of women and one man in this Rajasthani town who took up the offer of a free sterilisation operation to ensure their families got no larger. On its completion, each was given a coupon for a forthcoming raffle, with prizes including a Tata Nano car, motorbikes and electric food blenders. "I don't want any more children. It would be a burden to raise more children," a dazed Ms Kumar said after she blearily emerged from surgery. "I decided to have this done to make it easier."

India's population is huge and growing. The UN estimates that by 2050 it will have overtaken that of China and risen from its current 1.2 billion to more than 1.5 billion. In a country where there is already intense pressure on resources and opportunities, especially in its densely crowded cities, analysts have warned of the massive challenges this population will present.

But the country's efforts at confronting the issue have had mixed and often deeply controversial results. In the 1970s, Sanjay Gandhi, son of the then prime minister Indira Gandhi, oversaw a programme enacted during the State of Emergency in which unknown numbers of women were forced to be sterilised and men made to have vasectomies. Despite the turmoil and bad publicity created by his programme, today in many communities in India, especially in poorer, rural areas, sterilisation remains the preferred, and often only, form of contraception.

Technically, paying people to undergo the operations is illegal. But the Ministry of Health has established a scheme that pays those who have the procedure for "loss of earnings". A man receives 1,100 rupees (£15) while a woman pockets 600. Anyone who brings willing patients to the clinic – a so-called "motivator" – pockets 200 rupees.

Aparajita Gogoi, of the Centre for Development and Population Activities, a Delhi-based NGO, said while India had earned international criticism for its reliance upon sterilisation, in many communities family planning was not socially acceptable. "When it comes to availability of family planning, the issues of girls' education and the status of women in that community are interlinked," she said. "The biggest problem is that people do not have access to information about family planning and the services available."

The authorities in the Jhunjhunu district of Rajasthan, about 100 miles north of Jaipur, have long operated a programme of "camps" where men and women are made aware of the potential benefits of family planning and told that free sterilisation procedures are available. But during the monsoon months of July, August and September, officials noticed that the number of participants fell sharply; people were too busy in the fields and they were also concerned about a perceived risk of infection during the damp, humid weather.

This year, officials hit upon the idea of "incentivising" people to come forward during these three months, with the chance to win a series of prizes. Although a number of NGOs do not approve of the scheme, officials say they are doing nothing wrong. The prizes have all been donated by a local university.

Sitaram Sharma, the chief medical officer of the district, said there was a statewide target to sterilise 1 per cent of the population. "Last year around 10,000 people had the operation [in Juhnjhunnu district], but the target was 16,000. This year the target is 21,000 but I don't think we will reach it," he said.

"The awareness about birth control is very low." One day last week, doctors set up shop in the basic government clinic in Buhana, one of 39 such camps planned for the district in August. "We have 10 ladies and one man today; 99 per cent of the time they are women," said the surgeon, Sumair Singh Dhankar, who estimated that the operation took just three minutes for a woman and seven for a man.

The volunteers told similar stories. Rising prices of everything from wheat to diesel to vegetables had made them think, perhaps for the first time, about the size of their families. Surinder Singh, 57, from Bamanwas, a village about six miles away, had accompanied his daughter-in-law. Whereas Mr Singh had had five children, his son and daughter-in-law believed two was sufficient. "The control of the population should start now," he said, underscoring the generational change in attitudes.

Bhateri Devi had come with her sister-in-law, who was lying on a blanket laid out on the walkway outside the operating room, gradually rousing herself from the anaesthetic. The clinic, painted the colour of summer straw, had just a small recovery room, so many women had to lie outside until they came around, their friends and relatives flicking away flies with the snap of a scarf. Ms Devi, who has five children, said: "When I had my children, I did not have to worry about feeding them, but these days there are many price rises, for vegetables, sugar, the rent."

Mr Kumar, who had brought his wife to be sterilised, told a similar story about concern over rising prices and how they would manage to feed more mouths than the girl and boy they already had. He insisted he had only learned about the raffle to win a car once they had reached the hospital. Asked why his wife had the operation rather than him, he replied that he intended to return and have it done as well. When officials explained with a laugh why it was not necessary, he insisted: "I have the right to have it done and to collect the money."

After his wife emerged from the recovery area – a plain, windowless room with blankets laid on the floor and no beds – she was helped to stagger to a car waiting to take them back to their village.