Spend the remainder of the day recovering from your journey with a leisurely swim in the hotel pool, and perhaps a stroll around the local neighbourhood.

Cycle-rickshaws are a relaxing, and eco-friendly, way to explore the lanes of Old Delhi. Different streets are to be given over to different trades in this atmospheric district, which formed the hub of the Mughal city. Dominating its skyline is the massive white dome of the Jama Masjid mosque, the next stop on your tour. After admiring the extraordinary view from its minarets, enjoy lunch at one of the famous kebab restaurants below, before driving past the Raj-era capital to Humayun’s Tomb, one of the India’s greatest early Mughal buildings. Older still is the iconic Qutb Minar victory tower on Delhi’s southern outskirts, the day’s final stop.

An early start is required to catch the Gatimaan Express, which takes a little over an hour to reach Agra from Delhi. On arrival, you’ll be driven to the city’s great Mughal Fort, where Shah Jahan, creator of the Taj Mahal, was imprisoned at the end of his life by his son, Aurangzeb. On the opposite bank of the Yamuna River, the exquisitely decorated Itimad-ud Daulah tomb provides the next stop. The mausoleum’s inlay work foreshadowed that of the Taj, which you’ll visit towards the end of the afternoon, when the changing light transforms the marble surfaces from a pale ochre to orange and crimson.

The first stop on the fifth day of your tour is Fatehpur Sikri, the former capital of Emperor Akbar. It was built at lavish expense at end of the 16th century but only occupied for sixteen years. The finely carved, dark-red sandstone buildings remain in fine condition and vividly evoke the opulence of the Mughal era. Among many highlights are the Diwan-i-Khas audience hall, with its richly carved throne pillar, the beautiful Tomb of Sheikh Salim Chishti (a revered Sufi mystic) and Buland Darwaza gateway.

On arrival in Ranthambore you’ll check into your luxury hotel in time for the evening game drive around the park.

A former royal hunting reserve, Ranthambore nestles at the foot of a dramatic escarpment crowned by a ruined fortress. Expanses of grassland, marsh, lakes and mixed deciduous forest enfold the rocky plateau – perfect terrain for tiger and the herds of sambar deer and other animals they prey on. Just over 60 big cats currently prowl the park and your chances of a sighting a very good. Apart from tigers, Ranthambore also supports thriving populations of leopard, sambar and chital deer, nilgai (blackbuck), bears, crocodiles, and two species of monkey. Safaris are conducted in open-topped Jeeps.

After your early morning game drive and breakfast at Ranthambore, you’ll drive north towards the Rajasthani capital, Jaipur, skirting outliers of the Aravalli mountains along the way. Glimpses of rural life in the state enliven the journey across this quintessential Rajasthani landscape.

You’ll arrive at Jaipur in time for a leisurely exploration of the neighbourhood around your hotel, or a trip into the bazaar district. The capital abounds with places to sample traditional cuisine, as well as more cosmopolitan fare, and many restaurants lay on folk music and dance as post-prandial entertainment.

Perched on the rim of a dramatic escarpment overlooking a lake, Amber Fort retains some of the finest interiors surviving from the 16th and 17th centuries in India, notably a glittering ‘Hall of Mirrors’, or ‘Sheesh Mahal’, lined with intricate mirror mosaics where the Maharaja and his consorts would enjoy music and poetry recitals. Anyone interested in traditional Rajasthani textiles will also enjoy the Anokhi Museum of Hand Printing, located in a beautifully restored haveli in Amber village.

Jaipur itself is a swirl of life and colour, and its numerous monuments and markets provide the focus for the rest of the day. You’ll begin at the famous City Palace complex, which includes the much photographed ‘Hawa Mahal’, or ‘Palace of Winds’, a five-storey façade of elaborately screened windows from where the women of the royal household used to watch processions in the streets below.

Consider a visit to the gem market, where semi-precious stones from across Asia are polished and set in silver. The city also holds large branches of the Fab India department store and Anokhi, an international chain specializing in women’s clothes made from traditional Rajasthani textiles. There are also some fabulous palace hotels you may wish to visit: the Polo Bar at the Rambagh is welcoming place for a sundowner.