3 questions..please explain

[Shipra]

Can anyone please explain these questions to me? the answers are merked with (*)

1)Machine M can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
(A) 1/2
(B) 1/3(*)
(C) 4/13
(D) 8/29
(E) 6/33

2) Charmaine spent 2/5 of her income in January for rent, and 3/4 of the remainder on other expenses. If she put the remaining $180 in her savings account, how much was her income in January?
(A) $1,000
(B) $1,200(*)
(C) $1,400
(D) $1,600
(E) $1,800

3)A racetrack bound by two concentric circles, one with a diameter of 160 yards and the other with a diameter of 140 yards, is to be covered with asphalt. If the asphalt layer is to be one foot deep, how many cubic yards of asphalt will be needed?
(A) 75
(B) 90
(C) 500(*)
(D) 1500
(E) 2000

Thanks ,
Shipra [^]

[neetu08]

Hi
let me try(i'm not sure!).....

1. lets assume m/c N can produce x units in n time. so
m/c units time
----- -------- -------
M x 3/4(n)
N x n
O x 3/2(n)
now M/c M works at a rate of 4/3n of x units per hr(assume hr).
M/c N works at a rate of 1/n of x units per hr.
M/c O works at a rate of 2/3n of x units per hr.
therefore , if all the 3 m/c work together they should compete at the rate of

4/3n + 1/n + 2/3n = 9/3n = 3/n of x units per hr.
so they will produce x units in 1/3(n)hr
in 1 hr they will produce 3/n (x) units.
and in 1hr total units produced by m/c N = 1/n(x) units
therefore fraction of total output produced by m/c N is = (x/n)/(3x/n)
= 1/3


2. lets take total income of Charmaine is $x
so rent = 2x/5
other expenses = 3/4 of remainder = 3/4(x-2x/5)
= 3/4(3x/5)
= 9x/20
total expenses = 2x/5 + 9x/20
= 17x/20
now money left = x - 17x/20
= 3x/20
so 3x/20 = 180
x = 1200

3. there r 2 concentric circles with radius 80 yd and 70 yd
so area of intersection is = pi*R*R - pi*r*r
= pi(R*R - r*r)
= pi(80*80 - 70*70)
= 1500pi
now depth of asphalt is 1 foot = 1/3 yd
so total amount of asphalt used is = 1500pi * 1/3
= 500pi

but in the answer there in no pi ooppssss
please help!!

[Shipra]

Thanks Neetu08

I was also confued by the same in Que 3. I guess the answers are stated wrong. I took these questions from test#2 posted in the forum. This could be a typo. Hope so!!!

well thanks for the other 2 questions.

Shipra [^]

[Alexey_K(LexxRuss)]

the 3rd:
~1500 cubic yards
or 500pi cubic yards

[sdanquah]

With the first question, it is always advisable to pick numbers. The first number to pick shd be for O.
assumed number of hrs O can complete job is 6hrs
it means number of hrs N will take to complete same job = 2/3 x 6 =4
Number of hrs M will take = 3/4 x 4 = 3
if bot wotk together in 1 hr, M completes 1/3, N=1/4 and 0=1/6