Ramesh works A hours a day and rests B hours a day. This pattern continues for 1 week, with an exactly opposite pattern next week, and so on for four weeks. Every fifth week he adopts a new pattern which then continues for the next four weeks. When he works longer than he rests, his wage per hour is three times what he earns per hour when he rests longer than he works. The following table shows his daily working hours for the weeks numbered 1 to 13. | 1st Week | 5th Week | 9th Week | 13th Week Rest | 3 | 4 | 5 | - Work | 6 | 8 | 9 | 8 A week consists of six days and a month consists of four weeks. If Ramesh is paid Rs. 60 per working hour in the 1st week, what is his salary for the 1st month? (Assume that he is paid half his wages for his resting hours on duty)

Two pipes A and B can fill a cistern in 120 minutes and 150 minutes respectively. There is also an outlet C. If all the three pipes are opened together, the cistern gets filled in 100 minutes. How much time will be taken by C to empty the full tank?

In a box, there are eight yellow and four black balls. If three balls are drawn at random, what is the probability that two are yellow and one black?

Rakesh covers 12 km at 6 km/hr, 36 km at 9 km/hr and then 32 km at 4 km/hr. Find the approximate average speed in covering the whole distance.

If tan A + cot A = √5, what is the value of tan³A + cot³A?

If (x + 4) is a factor of x³ + 2x² + bx + 68, what is the value of b?

Two balls were bought for Rs. 37.40 at a discount of 15%. What must be the marked price of each of the balls?

The length of the minute hand of a watch is 42 mm. The area swept by it in 30 minutes (in mm²) by taking π as 3.14 is:

Find the value of a, if: |2a − 3| = 3a + 2