For first 5 hours, the doctor gets 10,000 and for every extra hour of work, he/she will get ₹500. If a doctor works for a hours and total amount paid to doctor for 1 day is Ty, then based on the above information, answer the following questions:
(a) The linear equation formed from the above situation is (0) y=10000+500x
(iii) y=10000+500(x-5)
(ii) y=500\times 1000x
(iv) y=10000\times(x-5)+500
(b) The standard form of linear equations formed is
(i) 500x+y-7500=t
(ii) 500x+y+7500=0
(iii) 500x-y+7500=0 (iv) x+500 y-7500=0
(c) The shape of the graph of a linear equation in two variables is
(i) circle (ii) parabola (iii) polygon
(d) The number of solutions of the linear equation formed is
(i) one (ii) two (fit) infinite (iv) line (v) none
(e) If a doctor works for 8 hours, then the amount paid to the doctor is
(i) 11,500 (ii) 10,500 (H) 14,000 (iv) 78,500
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Answers
SOLUTION
TO CHOOSE THE CORRECT OPTION
For first 5 hours, the doctor gets 10,000 and for every extra hour of work, he/she will get ₹500. If a doctor works for x hours and total amount paid to doctor for 1 day is y, then based on the above information, answer the following questions:
(a) The linear equation formed from the above situation is
(i) y = 10000 + 500x
(ii) y = 500 × 1000x
(iii) y = 10000 + 500(x-5)
(iv) y = 10000 × (x-5) + 500
(b) The standard form of linear equations formed is
(i) 500x + y - 7500 = t
(ii) 500x + y + 7500 = 0
(iii) 500x - y + 7500 = 0
(iv) x + 500y - 7500 = 0
(c) The shape of the graph of a linear equation in two variables is
(i) circle
(ii) parabola
(iii) polygon
(iv) line
(d) The number of solutions of the linear equation formed is
(i) one
(ii) two
(iii) infinite
(iv) none
(e) If a doctor works for 8 hours, then the amount paid to the doctor is
(i) 11,500
(ii) 10,500
(iii) 14,000
(iv) 78,500
EVALUATION
The doctor works for x hours and total amount paid to doctor for 1 day is y
(a) Now it is given that for first 5 hours, the doctor gets 10,000 and for every extra hour of work, he/she will get ₹500
So the linear equation formed from the above situation is
y = 10000 + 500( x - 5 )
Hence the correct option is
(iii) y = 10000 + 500(x-5)
(b) The equation can be rewritten as
y = 10000 + 500(x-5)
⇒ y = 10000 + 500x - 2500
⇒ y = 500x + 7500
⇒ 500x - y + 7500 = 0
So the standard form of linear equations formed is 500x - y + 7500 = 0
Hence the correct option is
(iii) 500x - y + 7500 = 0
(c) Highest power of x = 1
Highest power of y = 1
So the shape of the graph of a linear equation in two variables is a line
Hence the correct option is (iv) line
(d) We know that a linear equation has infinite number of solutions
So the number of solutions of the linear equation formed is infinite
Hence the correct option is (iii) infinite
(e) The doctor works for 8 hours
So x = 8
Thus the amount paid to the doctor
= 10000 + 500 × (8 - 5)
= 10000 + 1500
= 11500
Hence the correct option is (i) 11,500
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