11
Q:

# There are three boats B1, B2 and B3 working together they carry 60 people in each trip. One day an early morning B1 carried 50 people in few trips alone. When it stopped carrying the passengers B2 and B3 started carrying the people together. It took a total of 10 trips to carry 300 people by B1, B2 and B3. It is known that each day on an average 300 people cross the river using only one of the 3 boats B1, B2 and B3. How many trips it would take to B1, to carry 150 passengers alone?

 A) 15 B) 30 C) 25 D) 10

Explanation:

Combined efficiency of all the three boats = 60 passenger/trip

Now, consider option(a)

15 trips and 150 passengers means efficiency  of B1 = $\inline \fn_jvn 10\frac{p}{t}$

which means in carrying 50 passengers B1 must has taken 5 trips. So the rest trips equal to 5 (10-5 = 5) in which B2 and B3 together carried remaining 250 (300 - 50 = 250) Passengers.

Therefore the efficiency of B2 and B3 = $\inline \fn_jvn \frac{250}{5}=50\frac{p}{t}$

Since, the combined efficiency of B1, B2 and B3 is 60. Which is same as given in the first statement hence option(a) is correct.

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

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.

10 249
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

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

11 316
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

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.

7 174
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

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

7 232
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

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