What sum will give Rs 244/- as the difference between simple interest and compound interest at 10% pa in 1½ years compounded half-yearly?

Find the value of \(7875 \times 4574 \times697 \over82\)

Pipes A and B can fill a tank in 4 hours  and 6 hours 40 minutes, respectively; whereas a third pipe C can empty the full tank in 1 hours 40 minutes. A and B are opened at 2:00p.m. and 3:00 p.m., respectively and C is opened at 4:00 p.m. The tank will be completely empty at:

If a = 42 and b = 18, the value of a(a² - 3a + 3) - b(b² + 3b + 1) is