The Ramayana

RATIO AND PROPORTION 

The Ramayana narrates that Sita - the wife of Rama, prince of Ayodhya and avatar of the god Vishnu - was kidnapped by Ravana, the rakshasa (demon) king of Lanka.  On his way to Lanka, Rama met the brave Vanar leader Sugriva, who pledged alliance to him. Sugriva was helped by Rama to win the kingdom over from Bali, a mighty warrior king. As Rama marched ahead with his new Vanar Sena, He was faced with many challenges on the way. 

1. The Vanar Sena took with them food for 12 days. On the 4th morning of the journey, while getting ready to prepare the meals for the army, the head cook realized that 20% of the food left was spoiled due to high heat. If each Vanar ate 400 grams of food each day, what should be their new food ration per day per Vanar to survive the 12 days.

2. If they got tired on the way due to reduced food intake for 4 days, and calculated that they still had 8 more days to travel, by how much should they increase or decrease their food intake.   

3. 2 days away from the seas shore, they would smell the salty ocean winds and got energized again and started marching ahead very fast. They plan to complete the remaining trip in half the time, and so, want to consume 400 grams of food (as originally planned) for that extra boost of energy. How much food will remain as excess or fall short by the time they reach the shore?   

4. If the Vanar Sena had 5000 more foot-warriors, they would have had to carry 5% more food than they did. What was the strength of the Vanara Sena?

The Vanar sena marched ahead after overcoming each hurdle with proper planning, teamwork and trust in their leaders. Rama, aided by the army of Vanaras (monkeys), reached the end of land and wanted to cross over to Lanka. Rama worships the god of the ocean, Varuna, and requests him to make way. When Varuna does not appear before Rama, Rama plans to take the initiative and work a way around it. He shoots many arrows sequentially towards Lanka, with ropes attached to check the depth of the sea at different points. They make a map based on the lowest depth points that a third of the arrows shot hit, and plan to build a bridge above it. The construction started where the first arrows hit the points closest to the southern tip of India, and proceeded further as the last arrows hit the northern tip of Lanka. Coincidentally, the number of arrows shot, and the number of arrows that hit the desired shallow targets were divided equally among both north and south sides of the dam. The total length of the bridge is to be divided equally along the north and the south sides of the map. 

1. If the Vanars would collect 0.5 tons of pebbles, 1.2 ton of rock and 1.5 tons of dirt to be put for each point where Rama’s arrow hit the ground, then how many tons of rock and dirt were poured on for the 300 arrows that Rama shot.  

2. As a temporary dam begun to emerge, it seemed as if the Arabian sea would get split in half. If 40 tons of pebbles were on the north side of the dam, then how many tons of dirt fell into the south side of the dam?   

3. The strong under-currents in the Arabian sea washes off 2.5 tons plus 10% of the dirt for the first 50 arrows shot, and 15 kgs plus 20% of the dirt for each arrow shot after that. Then what is the ratio of Rocks to Dirt on the north side of the dam?   

4. If the Arabian sea washes off 10% of the dirt for the first 50 arrows that hit either side of the dam, and 25% of the total dirt present for every other arrow, then what is the ratio of Rocks to Dirt on the South side of the dam.  

TIME AND WORK 

But that bridge would also act as a dam and separate the Bay of Bengal from the Indian Ocean. A terrified Varuna pleads to Rama to find another way. Though Varuna refuses to give way, he gives Rama a solution. He tells Rama that Nala, the son of Vishwakarma - the architect of the gods, is amongst his Vanara army; Nala has the necessary expertise of an architect, owing to a boon from his divine father. Varuna suggests that Rama construct a bridge across the ocean to Lanka, under the supervision of Nala. The bridge would allow the sea to stay connected and not be split by a dam. Nala volunteers for the task and sets the work in motion. The Vanaras fell mighty trees, and collect logs of wood and giant boulders and cast them in the sea. He also uses the porous rocks plentily found in Rameshwaram to give additional buoyancy to the logs which might otherwise sink when the Vanar sena passes over. With the help of the Vanara army, Nala completes the 80 miles (130 km) (ten yojana) bridge in just five days.  

1. If 20 Vanagers or 100 forevanars or 400 transport Vanars can complete 0.2 miles of the bridge in 1 day, then how many miles of the bridge can be made by each of the current teams of 30 vanagers, 50 forevanars and 600 transport Vanars in 3 days?  

2. If the efficiency of Vanagers increases by 50% and that of forevanars increase by 25% after the second day of work when Hanuman inspires the teams with tales of lord Rama, then what is the minimum number of teams needed to complete the bridge in 5 days?   

3. If at the end of third day’s work it is decided that 200 transport Vanars per team will be shifted to the forests for logging, then how many more Vanagers need to be added to the teams so that the team composition is same across all teams and the progress of the work stays on course as planned?   

4. When 200 transport Vanars per team were shifted to the forests for logging, Nala found out that there was a shortage of Vanagers to replace them as planned initially. It was decided that for every replacement Vanager that moves into a team, 4 replacement Forevanars will also join that team. How many Vanagers are there in total in all the teams?     

TIME SPEED DISTANCE 

Rama and his army pass over the sea bridge (Ram Sethu) and reach Lanka, where they prepare to fight Ravana. Lakshmana gets seriously injured during his battle against Ravana’s son, Indrajit. Rama sends Hanuman to fetch a potent life restoring herb, Sanjivani, from the Dronagiri Mountains, which was twenty-five hundred kilometers away in the Himalayas. 

1. If Hanuman travelled the first 50% of his journey at half the speed as the next 50%, then at what fraction of time did he reach the Himalayas as compared to if he had continued at his ‘normal speed’, ie. the speed at which he started?  

2. Hanuman zooms till the foot of the mountain, 8 kms away. If the Sanjivani was to be found at a height of 6 kilometers through 8 kilometers in the Dronagiri Mountains, then what was the difference between the minimum to maximum time that Hanuman could have taken to get to the Sanjivani? 

3. If Hanuman covered the entire traveling part of the trip in 10 hours, to and from the base of the Dronagiri Mountains, and while on this way back, he came at twice his normal speed, then what was his normal speed, i.e. the speed at which he flew to the mountain?  

PERMUTATION AND COMBINATION 

Ravana, on hearing this, plans for Lakshmana’s death, as that would get Rama too grief-stricken to be able to fight in a war. He dispatches the witch Kalanemi to disrupt Hanuman’s attempts at finding the herb on time. Kalanemi, in disguise, as a sage, initially succeeds in fooling Hanuman.  

1. When Hanuman reaches Dronagiri, he finds many different flowers that resemble what he was told about the Sanjivani. He picks the 6 different flowers that match closest to his perception of Sanjivani and puts each of them into 5 boxes tied to his waistband. In how many ways can he put the flowers in the boxes if each box may hold 0-6 flowers?  

2. Kalanemi, in the sage disguise, advises Hanuman to look for Sanjivani in a small patch of the mountain where there are 4 types of green flowers, 4 types of blue flowers, 6 types of pink flowers and 5 types of yellow flowers, then: 

a. In how many ways can Hanuman choose 6 flowers so that he has all 4 coloured flowers?  

b. In how many ways can Hanuman choose 6 flowers of 4 different colours, including 3 yellow flowers? 

c. If Hanuman picks up 2 green and blue flowers each, and 3 pink and yellow flowers each; then how many different colour-combination garlands can he make from those flowers?  

d. If Hanuman finally decides that he would want to keep the same colour flowers together, then how many combinations garlands will he have to work out to see which colour combination he likes best?  

e. If Hanuman picks up 2 unique types of green and blue flowers each, and 3 unique types of pink and yellow flowers each; then how many different combinations of garlands can he make from those flowers?  

SPACE AND DIRECTION  

However, Hanuman finds out the disguise with the help of an apsara, whom he released from her accursed state of a crocodile, and he then defeats Kalanemi. Ravana, still doesn’t gives up on his attempts, and calls upon Surya to rise earlier than its schedule, Ravana knew that Lakshmana would succumb to his wounds if not treated till daybreak. Hanuman, on realizing this danger, transforms himself into many times his normal size, to prevent the Sun God from appearing. And then as he continued his search for the precious herb, he realized that he was not being able to recognize the specific herb that was required to cure Lakshmana. So, as a solution to his problem he lifts the entire mountain, owing to his infinite strength, and places the mountain in the battlefield of Lanka, where Sushena, the physician identifies the herb and uses it successfully to redeem Lakshmana back to life. Rama was ever grateful to Hanuman, and warmly embraced Hanuman to save his dear brother. Hanuman, then released Surya from his powerful grip, and asked for his forgiveness, as Surya was his teacher. 

1. Hanuman wanders around looking for the Sanjivani. He goes 100 meters north-west to and finds nothing. He then moves 60 meters south to find a well, where he takes a moment’s rest and has some water. From there he travels another 140 meters towards east by flying, before taking a turn in the south-west direction for 100 meters. How far is Hanuman now from the point where he started?  

2. If Kalanemi tries to escape from Hanuman by running east for 30 meters and then taking a sharp left and running 10 meters, then taking a sharp right and running for 90 meters and then again taking a sharp left continuing for 40 meters. If she plans to keep doing this confusing cycle of running for another 10 cycles before she can vanish using a magical spell, then how much distance should Hanuman cover to catch her mid-way through her run?   

3. If Hanuman could traverse the near circular breadth of the Dronagiri mountain (from the point where he was standing) in 2 minutes, then what was the approximate angle between his position at 60 seconds and at 90 seconds, from the point where he started?   

4. To keep Surya under check, Hanuman knows he cannot fly directly to Laxman. Also, to prevent the flowers from getting damaged due to wind turbulence, Hanuman decided to go higher up into the atmosphere. If the mighty Hanuman lifts the Dronagiri mountain and flies at an angle of 60 degrees against the axis joining Dronagiri’s original location and where Laxman awaits, then what is the speed of earth’s rotation if Hanuman reaches Laxman in just 156 minutes?