If 10 men and 15 women can do a piece of work in 8 days and 9 men and 12 women can do it in 9 days,

M4maths Previous Puzzles

04 Sep 2018 Work & Time

If 10 men and 15 women can do a piece of work in 8 days and 9 men and 12 women can do it in 9 days,

how many days will 5 men and 15 women take to do it?

OPtion

1) 14.75
2) 14.50
3) 14.33
4) 14.66
5) 14.20
6) 13.20
7) 13.33
8) 13.75
9) 14.40
10) None of these

Solution

Let a man's daily work is x units and that of a woman is y units.
So total amount of work, W = 8(10x + 15y) = 9(9x + 12y)

Solving we get, 80x - 81x = 108y - 120y
=> x = 12y



Now, 10 x + 15 y can do work in 8 days.
So, 120y + 15 y can do work in 8 days.
So, 135 y can do work in 8 days.

Now, 5x + 15y = 60y + 15y = 75y

Hence, if 135y can do work in 8 days, 75y can do work in (135*8)/75 = 14.4 days.

Option 9)

Correct Option: 9 Best Solution (9)

G.S.Kantharao   6 years AGO

10m+15w=8d
80m+120w=1d
9m+12w=9d
81m+108w=1d
81m+108w=80m+120w
1m=12w
10m+15w=120w+15w=135w =8d
5m+15w=5*12w+15w=xd
x=8*135/75=8*9/5=72/5=14.4d
Hence my option is 9👈

Like? Yes (3) | No   

anupama   6 years AGO

One day work
10M+15W=1/8---(1)
9M+12W=1/9----(2)
(1)-(2)--->M+3W=1/72
on multiplying by 5,we get
5M+15W=5/72
entire work=72/5=14.4

Like? Yes (2) | No   

ruby   6 years AGO

Given,
10m+15w=8days
9m+12w=9days
Total Work
8(10m+15w)=9(9m+12w)
1m=12w
Apply in 1st 10*12w+15w=1/8
135w=1/8 -----> 1w=1080
Question
5*1w+15w=75w=1080/75=14.40
Hence Option 9

Like? Yes (1) | No   

Vishnu Prakash   6 years AGO

10m+15w=1/8
9m+12w=1/9
On solving these two equations,
5m+15w=5/72
So, work is done in 72/5 = 14.4 days

Like? Yes | No   

Kariamal   6 years AGO

10m+15w=1/8...(1)
9m+12w=1/9.....(2)
From eq 1 and 2
w=1/1080
m=1/90
5m+15w=5/72=14.40

Like? Yes | No   

Shafigheh Nikpour   6 years AGO

let m=1 man-day
let w= 1 woman-day
1st equation:10(8)m+15(8)w=80m+120w=work done
2st equation: 9(9)m+12(9)w=81m+108w=work done
from 1 and 2 equation =>1m=12 w
so work done=80(12)w + 120w = 1080w
let' put the results in question:
5m[day]+15w[day]=5(12)w[day]+15w[day]=75w[day]=1080w
so the Answer is: day=1080/75=14.40

Like? Yes | No   

Prateek Mishra   6 years AGO

Because a MAN can do work equal to 12WOMEN.

Like? Yes | No   

SAYANTAN PATRA   6 years AGO

let the total work=lcm(8 and 9)=72
now 10 men 15 women can do 72/8=9 unit/day
and 9 men 12 women can do 72/9=8 unit /day
by substructing we can get 1 men 3 women can do 1 unit/day
now multiplying with 5 we can get
5 men and 15 women can do 5unit/day
so they complete 5 unit in 1 day
then 72 unit(whole work) in 72/5=14.40 days

Like? Yes | No   

Kaustubh S.   6 years AGO

work done by men and women per day is 1/x and 1/y
so
10/x+15/y=1/8
9/x+12/y=1/9
solving these two equation we get
X=90 , Y=1080
so substituting z and y in the required equation i.e
5/x+15/y=z
we get Z =14.40

Like? Yes | No