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Q:

# Raghu can complete a work in 12days working 9 hours a day. Arun can complete the same work in 8 days working 11 hours a day. If both Raghu and Arun work together, working 12 hours a day, in how many days can they complete the work ?A) $\inline \fn_jvn \small 3\tfrac{4}{49} days$    B) $\inline \fn_jvn \small 12\tfrac{4}{49} days$  C)  $\inline \fn_jvn \small 4\tfrac{3}{49} days$   D)  $\inline \fn_jvn \small 4\tfrac{12}{49} days$

 A) Option A B) Option B C) Option C D) Option D

Answer:   C) Option C

Explanation:

Raghu can complete the work in (12$\fn_jvn&space;\small&space;\times$9)hrs = 108 hrs.
Arun can complete the work in (8$\fn_jvn&space;\small&space;\times$11)hrs = 88 hrs.
Raghu's 1 hrs work = $\inline \fn_jvn \small \frac{1}{108}$ and Arun's 1 hrs work = $\inline \fn_jvn \small \frac{1}{88}$
(Raghu + Arun)'s 1 hrs work = $\inline \fn_jvn \small \left ( \frac{1}{108}+\frac{1}{88} \right ) = \frac{49}{2376}$
So, both Raghu and Arun will finish the work in $\inline \fn_jvn \small \left ( \frac{2376}{49}\right ) hrs$
Number of days of 12 hours each=$\inline \fn_jvn \small \left ( \frac{2376}{49}\times \frac{1}{12} \right )$ = $\inline \fn_jvn \small \frac{198}{49} = (4\tfrac{3}{49}) days$.

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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