Problema Solution
Ratan,Aditya,Kiran,Maya and monica contested an election . There were 1200 valid votes and no contestants other than these five . Maya got half the number of votes that Ratan and Aditya got . Kiran got half of the votes that the othere four got . Ratan,Kiran,Maya and Monica's votes together were thrice the number of votes that Aditya got . Ratan got one-fifth the votes that the others got . How many votes more that monica did Maya get ?
Answer provided by our tutors
Let
r = the number of votes that Ratan got
a = the number of votes that Aditya got
k = the number of votes that Kiran got
x = the number of votes that Maya got
y = the number of votes that Monica got
r + a + k + x + y = 1200
x = (1/2)(r + a)
k = (1/2)(r + a + x + y)
Since (r + a + x + y) = 1200 - k we have
k = (1/2)(1200 - k)
k = 600 - k/2
3k/2 = 600
k = 2*600/3
k = 400
(r + k + x + y) = 3a
Since r + k + x + y = 1200 - a we have:
3a = 1200 - a
4a = 1200
a = 1200/4
a = 300
r = (1/5)(a + k + x + y)
Since a + k + x + y = 1200 - r we have
r = (1/5)(1200 - r)
r = 240 - r/5
6r/5 = 240
r = 240*5/6
r = 200
Now we can find x:
x = (1/2)(200 + 300)
x = 250
From r + a + k + x + y = 1200 we find y:
y = 1200 - (r + a + k + x)
y = 1200 - (200 + 300 + 400 + 250)
y = 50
Since x - y = 250 - 50 = 200 the answer is: Monica got 200 more votes than Maya.