SOLUTION: 1. Rs. 6400 was divided among x persons. had this money been divided equally among (x+14) persons, each would have got Rs. 28 less. find the value of x 2) A number which when decr

Question 913220: 1. Rs. 6400 was divided among x persons. had this money been divided equally among (x+14) persons, each would have got Rs. 28 less. find the value of x
2) A number which when decreased by 20 is equal to 69 times the reciprocal of the number. find the number
3) If a train travels 15 km/hr faster, it would take 1 hours less to travel 180 km. find the original speed of the train.
4) A two digit number contains the smaller of the two digits in the unit's place. the product is 40 & the difference between the digits is 3. what is the number?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
1. Rs. 6400 was divided among x persons. had this money been divided equally among (x+14) persons, each would have got Rs. 28 less. find the value of x

When the number of persons are more each gets less
Total / number of persons = amount each gets
6400/x - 6400/(x+14) = 28
(6400(x+14)-6400x)/(x(x+14))=28
6400x +6400*14 -6400x = 28x(x+14)
6400*14 = 28x(x+14)
6400*14/28 = x+14
3200=x+14
3200-14=x
3186=x

2) A number which when decreased by 20 is equal to 69 times the reciprocal of the number. find the number
let number be x
x-20 = 69*1/x
x(x-20)=69
x^2-20x=69
x^2-20x-69=0
x^2-23x+3x-69=0
x(x-23)+3(x-23)=0
(x-23)(x+3)=0
x=23 OR -3

3) If a train travels 15 km/hr faster, it would take 1 hours less to travel 180 km. find the original speed of the train.
Same as (1)
let speed be x
180/x - 180/(x+15)=1
4) A two digit number contains the smaller of the two digits in the unit's place. the product is 40 & the difference between the digits is 3. what is the number?
let units place digit be y
ten's place digit be x
x-y =3...........................(1)
xy = 40
x=40/y
substitute in (1)
40/y -y = 3
40- y^2=3y
y^2+3y-40=0
y^2+8y-5y-40=0
y(y+8)-5(y+8)=0
(y+8)(y-5)=0
y=-8 OR 5
The number is 85
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