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- Question
A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
Options- A. 23 days
- B. 37 days
- C. 37½
- D. 40 days
- Correct Answer
- 37½
ExplanationWhole work is done by A in ❨ 20 x 5 ❩ = 25 days. 4 Now, ❨ 1 - 4 ❩ i.e., 1 work is done by A and B in 3 days. 5 5 Whole work will be done by A and B in (3 x 5) = 15 days.
A's 1 day's work = 1 , (A + B)'s 1 day's work = 1 . 25 15 ∴ B's 1 day's work = ❨ 1 - 1 ❩ = 4 = 2 . 15 25 150 75 So, B alone would do the work in 75 = 37 1 days. 2 2
More questions
- 1. Two pipes can fill a tank in 20 and 24 min, respectively and a waste pipe can empty 6 gallon per min. All the three pipes working together can fill the tank in 15 min. Find the capacity of the tank.
Options- A. 210 gallon
- B. 50 gallon
- C. 150 gallon
- D. 240 gallon Discuss
Correct Answer: 240 gallon
Explanation:
Part filled by 1st pipe in 1 min = 1/20
Part filled by 2nd pipe in 1 min = 1/24
Part filled by all the pipes in 1 min = 1/15
Work done by the waste pipe 1 min
= 1/15 - (1/20 + 1/24 )
= 1/15 - 11/120
= (8 - 11)/120 = ( - 3/120 ) = ( -1/40 )
[-ve sign indicates emptying]
Now, volume of 1/40 part = 6 gallon
? Volume of whole tank = 40 x 6 = 240 gallon
- 2. Two taps A and B can fill a tank in 20 min and 30 min, respectively. An outlet pipe C can empty the full tank in 15 min. A, B and C are opened alternatively, each for 1 min. How long will the tank take to be filled?
Options- A. 105 min
- B. 120 min
- C. 167 min
- D. 185 min Discuss
Correct Answer: 167 min
Explanation:
Part of the tank filled by the taps A, B and C in 3 min = 1/20 + 1/30 - 1/15 = (3 + 2 - 4)/60 = 1/60
? Time taken to fill [ 1 - ( 1/20 + 1/30 )] or 55/60th part of the tank = 3 x 55 = 165 min
Remaining part of the tank = 1 - 55/60 = 5/60 = 1/12
Tap A fill 1/0 part in 1 min, then
Remaining part = 1/12 - 1/20 = (5 -3)/60 = 2/60 = 1/30
i.e, 1/30th part is filled by B in 1 min
Hence, required time to fill the whole tank = (165 + 1 +1 ) min = 167 min- 3. Three taps A, B and C together can fill an empty cistern in 10 min . The tap A alone can fill it in 30 min and the tap B alone can fill it in 40 min. How long will the tap C alone take to fill it?
Options- A. 16 min
- B. 24 min
- C. 32 min
- D. 40 min Discuss
Correct Answer: 24 min
Explanation:
Part filled by (A + B + C ) in 1 min = 1/10
Part filled by A in 1 min = 1/30
Part filled by B in 1 min = 1/40
Part filled by (A+B) in 1 min = 1/30 + 1/40 = (4 + 3)/120 = 7/120
? Part filled by C in 1 min = 1/10 - 7/120 = (12 - 7)/120 = 5/120 = 1/24
? Tap C will fill the cistern in 24 min.- 4. Ramesh invested an amount that is 10% of ? 10000 at simple interest. After 3 yr, the amount becomes ? 2500. Find out the 4 times of actual interest rate.
Options- A. 5000%
- B. 250%
- C. 200%
- D. 600% Discuss
Correct Answer: 200%
Explanation:
Investment of Ramesh = 10% of 10000 = ? 1000
After 3 yr = 2500 - 1000 = ? 1500
We know.
SI = (P x R x T)/100
? 1500 = (1000 x R x 3)/100
? R = (1500 x 100) / (1000 x 3) = 50%
? 4 times of 50% = 200%- 5. The principle on which a simple interest of ? 55 will be obtained after 9 months at the rate of 3 2/ 3% per annum is
Options- A. 1000
- B. 1500
- C. 2000
- D. 2500 Discuss
Correct Answer: 2000
Explanation:
Let. principal = P
Given, SI = 55, Time T = 9 months = 9/12 yr,
Rate R = 32/3% = 11/3 %
? SI = (P x R x T) / 100
? P = (100 x SI) / (R x T)
? (55 x 100) / [(11 x 9) / (3 x 12)] = 2000
? Principal (P) = ? 2000- 6. A and B aim a target. The Probability that A hits the target is 5/7 and B hits the target in 7/10. What is the probability that exactly one of them hits the target?
Options- A. 21/10
- B. 29/70
- C. 31/70
- D. 33/70 Discuss
Correct Answer: 29/70
Explanation:
Required probability = P(A). P(B) + P (A ) . P(B)
= 5/7 . 3/10 + 2/7 . 7/10
= 29/70- 7. 40 men can build a wall 200 m long in 12 days, working 8h a day. What will be the number of days that 30 men will take to built a similar wall 300 m long, working 6h per days.
Options- A. 32
- B. 18
- C. 36
- D. 9 Discuss
Correct Answer: 32
Explanation:
Given, M1 = 40, W1 = 200, T1 = 8, D1 = 12,
M2 = 30, W2 = 300, T2 = 6 and D2 = ?
Then, using formula
M1T1D1W2 = M2T2D2W1
? 40 x 8 x 12 x 300 = 30 x 6 x D2 x 200
? D2 = (40 x 8 x 12 x 300)/(30 x 6 x 200) = 32 days.- 8. Ram finishes a work in 7 days. Rahim finish the same job in 8 days and Robert in 6 days. They take turns to finish the work. Ram worked on the first day, Rahim on the second day and Robert on the third and then again Ram and so on. Who was working on the last day when work got finished?
Options- A. Ram
- B. Rahim
- C. Robert
- D. Rahim and Robert Discuss
Correct Answer: Ram
Explanation:
Three day work or Ram, Rahim and Robert = 1/7 + 1/8 + 1/6
= (24 + 21 + 28)/168 = 73/168
Their six days work = (2 x 73)/168 = 146/168 = 73/84
Now, its Ram's turn to work on seventh day.
? 73/84 + 1/7 = 73 + 12/84 = 85/84 > 1
So, Ram will finish the work before the end of day.
Hence, Ram is working for the last day.- 9. If 12 man or 18 women can do piece of work in 14 days. How long will 8 men and 16 women take to finish the work?
Options- A. 9 days
- B. 12 days
- C. 13 days
- D. 10 days Discuss
Correct Answer: 9 days
Explanation:
12 men =18 women
? 1 man = 18/12 women
? 8 men = 18/12 x 8 = 12 women
Given m1 = 18 M2 = 12 +16 = 28,
D1 , D2 = ? and W1 = W2 = 1
According to the formula
M1D1W2 = M2D2W1
? 18 x14 x1= 28 x D2 x1
? D2 = (18 x 14)/28 = 9 days- 10. Rashim lent ? 600 to Geeta for 2 yr and ? 150 to Seeta 4 yr and received altogether ? 80 as simple interest from both. Find the rate of interest.
Options- A. 34/9%
- B. 24/9%
- C. 54/9%
- D. 44/9% Discuss
Correct Answer: 44/9%
Explanation:
Given. T1 = 2 yr and T2 = 4 yr,
P1 = 600, P2 = 150.
According to the question,
SI1 + SI2 = 80
[(600 x R x 2)/100] + [(150 x R x 4)/100] = 80
? 120R + 60R = 800
? 180R = 800
? R = 800/180 = 80/18 = 40/9
= 44/9%
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