a women has 10000 rupees with her. She calculated that she could spend x rupees on her holidays. she spent (x-50) rupees everyday and extended her holidays by 10 days. Calculate x?
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Let no. of days be 'y'
and ₹ spent daily be 'x'
ATQ
xy = 10000. eq.1
(x-50)(y+10) = 10000. eq.2
xy + 10x -50y - 500 = 10000
10000 + 10x -50y -500 = 10000
10x - 50y = 500
x-5y = 50
x = 50+5y. eq.3
Putting this value in eq.1
(50+5y)(y) = 10000
50y + 5y^2 = 10000
y^2 + 10y - 2000 = 0
y^2 + 50y - 40y - 2000 = 0
y(y+50) - 40(y+50) = 0
(y-40)(y+50) = 0
y cannot be equal to - 50 because days can't be negative so
y = 40
Putting this value in eq.3
x = 50 + 5(40)
x = 50 + 200
x = ₹250
and ₹ spent daily be 'x'
ATQ
xy = 10000. eq.1
(x-50)(y+10) = 10000. eq.2
xy + 10x -50y - 500 = 10000
10000 + 10x -50y -500 = 10000
10x - 50y = 500
x-5y = 50
x = 50+5y. eq.3
Putting this value in eq.1
(50+5y)(y) = 10000
50y + 5y^2 = 10000
y^2 + 10y - 2000 = 0
y^2 + 50y - 40y - 2000 = 0
y(y+50) - 40(y+50) = 0
(y-40)(y+50) = 0
y cannot be equal to - 50 because days can't be negative so
y = 40
Putting this value in eq.3
x = 50 + 5(40)
x = 50 + 200
x = ₹250
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