Quantitative Aptitude - Arithmetic Ability Questions

Compound Interest on P at 10% for 2 years when interest is compounded half-yearly

=P1+R21002T-P=P1+1204-P=P21204-P

Simple Interest on P at 10% for 2 years = PRT100=P×10×2100=P5

Given that difference between compound interest and simple interest = 124.05

 P*21204-P-P5=124.05

=>P21204-1-15=124.05

 P=8000

When B runs 25 m, A runs 45/2 m

When B runs 1000 m, A runs (45/2*1/25*1000)m = 900 m.

B beats A by 100 m.

There are 7 digits 1, 2, 0, 2, 4, 2, 4 in which 2 occurs 3 times, 4 occurs 2 times.

 Number of 7 digit numbers = 7!3!×2! = 420

But out of these 420 numbers, there are some numbers which begin with '0' and they are not 7-digit numbers. The number of such numbers beginning with '0'.

=6!3!×2! = 60

Hence the required number of 7 digits numbers = 420 - 60 = 360