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Question 13 Marks
A bill for Rs. 7650 was drawn on 8th March 2005 at 7 months. It was discounted on 18 May 2005 and the holder of the bill received Rs. 7497. What rate of interest did the banker charge?
Answer
$\text{S} = \text{Rs 7650 ; Legal due date is October 11 2005}$$\text{Date of discounting = 18 May, 2005}$
$\text{Time (t) = ( 13 + 30 + 31 + 31 + 30 + 11) days = 146 days = } \frac{2}{5}\text{years} $
$\text{B.D = (7650 - 7497) = Rs 153. Let r be rate percent per annum}$
$\therefore \frac{7650\times r}{100} \times \frac{2}{5} = 153$
$\Rightarrow = r = \frac{153 \times 250}{7650} = 5\text{%}$
$\therefore \text{rate of interest is 5%}$
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Question 23 Marks
Find the face value of a bill, discounted at 6% per annum 146 days before the legal due date, if the banker's gain is Rs. 36.
Answer
$\text{Here r} = 6\text{%} = \frac{6}{100}, t = \frac{2}{5} \text{year},\text{B.G} = \text{Rs 36} $$\text{B.G} = \frac{(srt)rt}{1 + rt}$
$\text{S} = Rs\Bigg[ 36 \bigg(1 + \frac{3}{125}\bigg) \bigg(\frac{125}{3}\bigg) \bigg( \frac{125}{3}\bigg) \Bigg]$
$= \text{Rs 64000}$
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Question 33 Marks
Determine the maximum value of Z = 3x + 4y if the feasible region (shaded) for a LPP is shown in.
Answer

As clear from the graph, corner points are O, A, E and D with coordinate (0, 0), (52, 0), (144, 16) and (0, 38), respectively. Also given is bounded.
Here, Z = 3x + 4y
$\because$ 2x + y = 104
and 2x + 4y = 152
solving above equations,we get
⇒ -3y = -48
⇒ y = 16 and x = 44
Corner points
Corresponding value of Z
(0, 0)
(52, 0)
(44, 16)
(0, 38)
0
156
196 (Maximum)
152
Hence, Z is maximum at (44, 16) and its maximum value is 196.
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Question 43 Marks
The feasible region for a LPP is shown in. Find the minimum value of Z = 11x + 7y.
Answer
Lines x + y = 5 and x + 3y = 9 intersect at (3, 2)
From the feasible region is bounded with corner points as c(0, 3), A(3, 2) and B(0, 5).
Also z = 11x + 7y
Corner points
Corresponding value of Z
(0, 3)
(3, 2)
(0, 5)
21 (minimum)
47
35
Hence, the minimum value of Z is 21 at (0, 3).
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Question 53 Marks
Feasible region (shaded) for a LPP is shown in Maximise Z = 5x + 7y.
Answer
The shaded region is bounded and has coordinates of corner points as (0, 0), (7, 0), (3, 4) and (0, 2). Also, Z = 5x + 1y.
Corner points
Corresponding value of Z
(0, 0)
(7, 0)
(3, 4)
(0, 2)
0
35
43 (Maximum)
14
Hence, the maximum value of Z is 43 at (3, 4).
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