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91. Find S.P., when:
(i) C.P. = Rs. 56.25, gain = 20%.
(ii) C.P. = Rs. 80.40, loss = 15%.
Solution:
(i) S.P. = 120% of Rs. 56.25 = Rs. (120*56.25/100) = Rs. 67.50.
(ii) S.P. = 85% of Rs. 80.40 = Rs. (85*80.40/100) = Rs. 68.34.
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92. A scooterist covers a certain distance at 36 kmph. How many meters does he cover in 2min?
Solution:
Speed = 36 kmph = 36 * 5/18 = 10mps
Therefore, Distance covered in 2 min = (10 * 2 * 60)m = 1200m
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93. A gentleman buys every year Bank's cash certificates of value exceeding the last year's purchase by Rs. 300. After 20 years, he finds that the total value of the certificates purchased by him is Rs. 83,000. Find the value of the certificates purchased by him in the 13th year.
Solution:
Let the value of the certificates purchased in the first year be Rs. a.
The difference between the value of the certificates is Rs. 300 (d = 300).
Since, it follows Arithmetic progression the total value of the certificates after 20 years is given by
Sn = n/2 [2a + (n - 1) d] = 20/2[2a + 19(300)] = 83,000.
By simplifying we get 2a + 5700 = 8300.
Therefore, a = Rs. 1300.
The value of the certificates purchased by him in nth year = a + (n - 1) d.
Therefore, the value of the certificates purchased by him in 13th year = 1300 + (13 - 1) 300 = Rs. 4900.
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94. How often between 11 O'clock and 12 O'clock are the hands of the clock together at an integral number value?
Solution:
At 11 O'clock, the hour hand is 5 spaces apart from the minute hand.
During the next 60 minutes, i.e. between 11' O clock and 12' O clock the hour hand will move five spaces [integral values as denoted by the 56 minute, 57 minute, 58 minute, 59 minute and 60 minute positions].
For each of these 5 positions, the minute hand will be at the 12th minute, 24th minute, 36th minute, 48th minute and 60th minute positions.
Hence the difference between the positions of the hour hand and the minute hand will have an integral number of minutes between them.
i.e. 5 positions.
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95. Given that on 27th February 2003 is Thursday. What was the day on 27th February 1603?
Solution:
After every 400 years, the same day occurs.
Thus, if 27th February 2003 is Thursday, before 400 years i.e., on 27th February 1603 has to be Thursday.
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