Who broke the penance of Sage Vishwamitra?

 Vishwamitra's penance was rendered void twice(Once broken , it needs to be started from beginning). Once by Menaka and the second time by Rambha.

In the First Case, Vishwamitra fell for Menaka's beauty and his lust overcame his desire for enlightenment. He spent 10 years with Menaka. Thereafter , he desired to do Penance again.

Then at a long lost time Menaka, the prominent apsara, celestial wench, has arrived and started to swim for sport in that holy lake. That great resplendent sage Vishvamitra has seen Menaka who is incomparable in her mien and comparable to an electric-flash in a black-cloud, while she is swimming in the holy lake. On seeing her the sage having gone under the sway of Love-god said this to her, 'oh, apsara, you are welcome, I invite you to bide in my hermitage. Oblige me who am bewitched by Love-god for you. You be safe.’

"When he said thus to her, oh, Raghava, then she made a stopover there and ten years rolled by comfortably, and oh, gentle Rama, because of her staying Vishvamitra is indeed faced with a great hindrance in his ascesis. Then after the lapse of that ten year period Vishvamitra became doleful with distress and he is enwrapped in humiliation, as it were, and, oh, Rama, Raghu's legatee, then a resentful thought occurred to him.

" 'All this is the mischief of gods to defraud me of the great merit of my ascesis. Ten years have rolled by as if they are just a day and a night. Furthermore, I who am under the influence of lust and lure had to encounter this hindrance in my ascesis.' Oh, Rama, that best saint suspired heavily when he became emotional with reparation. But on seeing the scared celestial wench Menaka, who is shivering and waiting with suppliantly adjoined palms, he sent her away with pleasant words, and he that Vishvamitra indeed went to the northern Himalayan mountain.

He started penance again. This time Indra send Rambha to disrupt his penance. Having understood intention of Rambha to Lure him again, Vishwamitra trembled in Wrath and Uttered a Curse transforming Rambha to stone. Because of his wrath, once again he Lost everything gained through Acsesis.

At the instance of Indra, that lovely nymph clad in enchanting raiment, faintly smiling, went forth to allure the heart of Shri Vishvamitra.

At that moment, the liquid notes of the cuckoo began to delight the rishi and he then beheld the nymph Rambha. Stirred by the cuckoo’s note and the ravishing sound of the beautiful Rambha’s song, Shri Vishvamitra, recollecting his former fall, was filled with misgiving and recognizing the design of the god Indra, transported with rage, cursed Rambha, saying:—

“O Rambha, O Unfortunate One, you have come hither to lure me from my penance, I, who have conquered lust and anger. Mayest you become petrified and take the form of a rock for ten thousand years. A brahmin perfected in the power of Yoga shall one day deliver you from this curse.”

Having pronounced this curse on Rambha, the rishi became a prey to remorse, for, giving way to wrath he lost the fruit of all his yogic practices.

In the Final try he succeeded and Became a Brahmarishi Conquering all His emotions and attachments to material items..

In which age did Vishwamitra teach Rama?

 Rama is stated to be less than 16 years old when he went with Vishwamitra. He stayed with Vishwamitra for less than a month.

My lotus-eyed Rama is still less than sixteen years of age. I do not see him as being capable of fighting against the rakshasas.

• 1 (19), Bala Kanda, Valmiki Ramayana.

Rama’s time with Vishwamitra

Day 1 - Rama and Lakshman leaves with Vishwamitra. Vishwamitra taught them Bala and Atibala mantra. The three spend the night on the banks of Sarayu.

Day 2 - They reached ashrama of Kama located at the confluence of Sarayu and Ganga and spent the night there.

Day 3 - The trio cross the river and reached a dense forest in it's southern bank. Here Rama slew the rakshasi Tataka. That night, they resided in the forest.

Day 4 - Vishwamitra imparts the knowledge of various Divyastras to Rama. The trio arrives in Siddhashrama.

Day 5 - Day 10 - Rama and Lakshman protects Vishwamitra’s sacrifice. On the final day, Rama slays Subahu and defeats Maricha.

Day 11 - Vishwamitra takes Rama and Lakshmana to Mithila to see Shiva’s bow. That night they camped near Shona river.

Day 12 - The trio camps at the banks of river Ganga. Vishwamitra narrates the story of the descent of Ganga.

Day 13 - The cross the river and arrived at the city of Vishala on its northern bank. They spent the night there.

Day 14 - The trio arrives in Mithila. Rama saves Ahilya. Janaka and others welcome the trio in Mithila. Narration of the story of Vishwamitra.

Day 15 - Rama breaks Shiva's bow and Janaka declares him as eligible to marry Sita. Messangers send to Ayodhya to invite Dasharatha for the marriage.

Day 18 - Janaka’s messangers arrive in Ayodhya and informed everyone of Rama’s success.

Day 23 - Dasharatha and royal party from Ayodhya arrives in Mithila.

Day 27 - Marriage of Rama and his brothers with Sita and her sisters.

Day 28 - Vishwamitra bids farewell and leaves for the mountains.