Ram Lal is a renowned packager of fruits in Varanasi. He packs 70 mangoes or 56 guavas every day working 7 hours a day. His wife also helps him. She packs 30 mangoes or 24 guavas working 6 hours per day. Ram Lal has to pack 3300 mangoes and 2400 guavas with help of his wife. They works alternately, each day 10 hours. His wife started packaging firs day and works every alternate days. Similarly, Ram Lal started his work second day and and worked alternatively till the completion of the work. In how many days the work will finished?

Explanation:-

Mango Packing rate of Ram Lal = $$\frac{{70}}{7}$$ = 10 per hour
Guavas Packing rate of Ram Lal = $$\frac{{56}}{7}$$ = 8 per hour
Mango Packing rate of Ram Lal's Wife = $$\frac{{30}}{6}$$ = 5 per hour
Guavas Packing rate of Ram Lal's Wife = $$\frac{{24}}{6}$$ = 4 per hour

On comparing,
8 Guavas = 10 Mangoes
1 Guavas = $$\frac{{10}}{8}$$ Mangoes
2400 Guavas = $$\frac{{10 \times 2400}}{8}$$   = 3000 Mangoes
This means that they need to pack (6300 + 3000) Mangoes

Combined Mango Packing rate of Both = 10 + 5 = 15 per hour

We will take 2 days = 1 time unit.
Working 10 hours a day they will pack 150 Mangoes in 1 time unit
Total time taken to pack 6300 Mangoes = $$\frac{{6300}}{{150}}$$   = 42 time unit
So, total time taken = 2 × 42 = 84 days