12
Q:

(x-2) men can do a piece of work in x days and (x+7) men can do 75% of the same work in (x-10)days. Then in how many days can (x+10) men finish the work?

A) 27 days B) 12 days
C) 25 days D) 18 days

Answer:   B) 12 days



Explanation:

\inline \fn_jvn \frac{3}{4}\times (x-2)x=(x+7)(x-10)

\inline \fn_jvn \Rightarrow    \inline \fn_jvn x^{2}-6x-280=0 

\inline \fn_jvn \Rightarrow    x= 20   and   x=-14

so, the acceptable values is x=20

\inline \fn_jvn \therefore Total work = \inline \fn_jvn (x-2)\times x = 18 x 20 =360 unit

Now   360 = 30 x k          \inline \fn_jvn \because (30=20+10)

\inline \fn_jvn \Rightarrow  k=12 days

Q:

P is 30% more efficient than Q. How much time will they, working together, take to complete a job which P alone could have done in 23 days?

A) 16 days B) 13 days
C) 15 days D) 12 days
 
Answer & Explanation Answer: B) 13 days

Explanation:

Ratio of times taken by P & Q = 100 : 130 = 10:13

Let Q takes x days to do the work

Then, 10:13 :: 23:x

=> x = 23x13/10

=> x = 299/10

P's 1 day's work = 1/23

Q's 1 day's work = 10/299

(P+Q)'s 1 day's work = (1/23 + 10/299) = 23/299 = 1/13

Hence, P & Q together can complete the work in 13 days.

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10 223
Q:

If 2 men and 3 women can do a piece of work in 8 days and 3 men and 2 women in 7 days. In how many days can the work be done by 5 men and 4 women working together?

A) 3 days B) 6 days
C) 4 days D) 2 days
 
Answer & Explanation Answer: C) 4 days

Explanation:

From the given data,

=> (2 M + 3W) 8 = (3M + 2W)7

=> 16M + 24W = 21M + 14 W

=> 10W = 5M

=> 2W = M

=> 14W × ? = 7W × 8

? = 4 days

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11 292
Q:

28 Men and 52 women working together completes a work in 22.5 days. 35 men and 65 women working together on same work will complete it in how many days?

A) 16 B) 18
C) 19 D) 21
 
Answer & Explanation Answer: B) 18

Explanation:

clearly total persons are increased in => 28/35 :: 52/65 = 4:5

As time is inversely proportional to men, so total time will decrease in the ratio 5:4

Hence, 22.5 x 4/5 = 18 days.

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6 157
Q:

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left?

A) 8/15 B) 7/9
C) 6/13 D) 4/11
 
Answer & Explanation Answer: A) 8/15

Explanation:
P's 1 day's work = 1  
15
Q's 1 day's work = 1  
20
(P + Q)'s 1 day's work = ( 1 + 1 ) = 7  
15 20 60
(P + Q)'s 4 day's work = ( 7 x 4 ) = 7  
60 15
Therefore, Remaining work = ( 1 - 7 ) = 8 .
15 15
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7 211
Q:

X can complete the work in 10 days, Y can do the same in 15 days. If they are hired for 5 days to do the work together, what is the work that left unfinished?

A) 1/3 B) 2/3
C) 1/6 D) 5/6
 
Answer & Explanation Answer: C) 1/6

Explanation:

Given X can do in 10 days

=> 1 day work of X = 1/10

Y can do in 15 days

=> 1 day work of Y = 1/15

1day work of (X + Y) = 1/10 + 1/15 = 1/6

Given they are hired for 5 days

=> 5 days work of (X + Y) = 5 x 1/6 = 5/6

Therefore, Unfinished work = 1 - 5/6 = 1/6 

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8 355