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Joint Recruitment for 4 Banks || Officer (General) (21-06-2019) || 2019

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গণিত


1.

6 men can complete a piece of work in 12 days. 8 women can complete the same piece of work in 18 days whereas 18 children can complete the piece of work in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work 1 day how many men would be required totally?
Created: 3 months ago | Updated: 3 weeks ago

1 man`s 1 day work =16×12=172part ∴1 woman 1 day work= 18×18=1144part ∴1 child 1 day work = 118×10=1180 part now, 4 men, 12 women and 20 children can do in 2 days =2(472+12144+20180) =872+24144+40180 =19+16+19  =918 =12part ∴Remaining work = 1-12=12 part Now, 172 part of work is done in 1 day by = 1 man ∴12 part of work is done in 1 day by = 72×12×1=36 men answer: 36 men.  


2.

First bag contains 4 red and 3 black balls. Second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.
Created: 3 months ago | Updated: 3 weeks ago

Probability that the first bag is chosen and a red ball is drawn = 12×43+4=12×47=27 Again, probability that the second bag is chosen and a red ball is drawn=12×26=16 ∴Probability of red =27+16=12+742=1942 (answer)


3.

A cow was standing on a bridge, Sm away from the middle of the bridge. A train was coming towards the bridge from the ends nearest to the cow. Seeing this, cow ran towards the train and managed to escape when the train was 2m away from bridge. If it had run in the opposite direction, it would hit by the train 2m before the end of the bridge. What is the length of the bridge in meters assuming the speed of the train is 4 times that of cow?
Created: 3 months ago | Updated: 3 weeks ago

Let, the distance of cow from the nearest end of bridge is x meters

∴Half length of the bridge is (x + 5)  meters

Now, assume that, the cow runs x meters in y seconds.

∴The train covers in y seconds = 4x meters.

Given, that the train was (4x + 2) meters away from the bridge when the cow saw the train.

Here, covering time of = x + 10 - 2 = (x + 8) meters distance by the cow is same covering time of

(4x + 2 + 2x + 10 - 2) = (6x + 10) meters distance covered by train.

Here, (x + 10) = Distance of cow from the far end to hit the cow.

( 4x +2)= Distance covered by the train to reach at the near end.

And (2x + 10 - 2) = Distance covered by train from near end.

∴ We can write, 4(x + 8) = 6x + 10

= 4x + 32 = 6x + 10

= 2x = 22

∴x = 11

∴ Length of the bridge = 2x+10= (2 x 11)+10=22+ 10 = 32 meters.


4.

A man went downstream for 28km in a motor boat and immediately returned. It took the man twice as long to make the return trip. If the speed of the river flow were twice as high, the trip downstream and back would take 672 minutes. Find the speed of the boat in still water and the speed of the river flow.
Created: 3 months ago | Updated: 3 weeks ago

5.

A, B and C started a business by investing Tk. 24000, Tk. 32000 and Tk. 18000 respectively. A 14 and B are active partners and get 15% and 12% of total profit and remaining profit is to be distributed among them in the ratio of their investment. If C got total Tk. 65,700 as a profit?
Created: 3 months ago | Updated: 3 weeks ago

Let, total profit= 100 Tk. 

∴Remaining profit=(100-15-12)%=73% 

Ratio of their investment = 24,000: 32,000: 18,000=12: 16:9

∴C's share of profit = (912+16+9×73)%=65737% of total profit

Now, according to question

65737% of total profit= 65,700 Tk.

∴100% of total profit=65700×37×100657=370000 tk

Answer: Total profit 3,70,000 Tk.

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