Aptitude - Time and Work - Discussion

Discussion Forum : Time and Work - General Questions (Q.No. 6)
6.
If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
4 days
5 days
6 days
7 days
Answer: Option
Explanation:

Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.

Then, 6x + 8y = 1 and 26x + 48y = 1 .
10 2

Solving these two equations, we get : x = 1 and y = 1 .
100 200

(15 men + 20 boy)'s 1 day's work = 15 + 20 = 1 .
100 200 4

15 men and 20 boys can do the work in 4 days.

Discussion:
193 comments Page 1 of 20.

Sangeetha said:   1 decade ago
Can you please solve these 2 equations and show me the result?
(1)

Meera said:   1 decade ago
Hi Sangeetha its very easy to solve this equations.

6x+8y=1/10 ----- (i)
26x+48y=1/2 ------(ii)

Multiply 1st equation into 6, then we get:
36x+48y=1/10*6
26x+48y=1/2

Change the sign of 2nd equation
36x+48y=3/5
-26x-48y=-1/2

The result is
10x=3/5-1/2
10x=1/10
x=1/100

Then apply x value into 1st equation
6x+8y=1/10
6*1/10+8y=1/10
8y=4/100
y=1/200

Thats it.
(2)

Siddharth said:   1 decade ago
No need to solve equation:

we have
6x+8y=1/10 ----- (1)
26x+48y=1/2 ------(2)

we want to find: 15x+20y=?----(3)
now taking 2 common form equ(1),
we get:
2(3x+4y)=1/10

So we have, 3x+4y=1/20...ok...
now
in equ 3, take 5 common;
we get:
=5(3x+4y) (3x+4y=1/20)
=5*(1/20)
=4 (ans)
(4)

Singh said:   1 decade ago
Siddu you are genious friend.

Arun said:   1 decade ago
There must be a faster way of doing this mentally. Like skipping the equation part. Some kind of approximation. Does anyone know?

Bharathi said:   1 decade ago
How 1/100+1/200=4 ?

Nagarjun said:   1 decade ago
@Bharathi.

Hey its not 1/100+1/200=4
Its (15/100)+(20/100)
This vl give 1/4, vch is 1 day's work, and finally they can complete it in 4 days.

Jyothi said:   1 decade ago
Hi siddu.

I'm jyothi. You are genious. Thanks friend.
(1)

Vicky said:   1 decade ago
@Sidhu

We want to find: 15x+20y=?----(3)
now taking 2 common form equ(1),

We get: 2(3x+4y)=1/10

So we have, 3x+4y=1/20...ok...///// if we take 2 common ok

2(3x+4y)ok but how u get = 1/20 hmmmmmm

Vicky said:   1 decade ago
2x+3y=1/10 ----- (1)
3x+2y=1/8 ------(2)

we want to find: 2x+1y=?----(3)
any one can solve this


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