86. The difference between the compound interest and the simple interest on a certain sum at 12% p.a. for two years is Rs.90. What will be the value of the amount at the end of 3 years?

Solution:
The difference in the simple interest and compound interest for two years is on account of the interest paid on the first year's interest, when interest is reckoned using compound interest, interest being compounded annually.
Hence 12% of simple interest = 90 => simple interest = =750.
As the simple interest for a year = 750 @ 12% p.a., the principal = = Rs.6250.

If the principal is 6250, then the amount outstanding at the end of 3 years = 6250 + 3(simple interest on 6250) + 3 (interest on simple interest) + 1 (interest on interest on interest) = 6250 + 3(750) + 3(90) + 1(10.80) = 8780.80.

87. How long will it take for a sum of money to grow from Rs.1250 to Rs.10,000, if it is invested at 12.5% p.a simple interest?

Solution:
Simple interest is given by the formula SI = (pnr/100), where p is the principal, n is the number of years for which it is invested, r is the rate of interest per annum
In this case, Rs. 1250 has become Rs.10,000.
Therefore, the interest earned = 10,000 – 1250 = 8750.
8750 = [(1250*n*12.5)/100]
=> n = 700 / 12.5 = 56 years.

88. If the wheel of a bicycle makes 560 revolutions in travelling 1.1 km, what is its radius?

Solution:
The distance covered by the wheel in 560 revolutions = 1100 m . Hence, the distance covered per revolution = metres. The distance covered in one revolution = circumference of the wheel.
Circumference = => r = 31.25 cm.

89. The time in a clock is 20 minute past 2. Find the angle between the hands of the clock.

Solution:
Time is 2:20. Position of the hands: Hour hand at 2 (nearly).
Minute hand at 4
Angle between 2 and 4 is 60 degrees [(360/12) * (4-2)]
Angle made by the hour hand in 20 minutes is 10 degrees, since it turns through ½ degrees in a minute.
Therefore, angle between the hands is 60 degrees - 10 degrees = 50 degrees

90.A man buys an article for Rs. 27.50 and sells it for Rs. 28.60. Find his gain percent.

Solution:
C.P. = Rs.27.50, S.P. = Rs. 28.60.
Therefore Gain = Rs. (28.60 – 27.50) = Rs.1.10.
Therefore Gain % = (1.10*100/27.50) % = 4%.