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Q:

Three numbers are in the ratio  1 : 2 : 3  and their H.C.F is 12. The numbers are

A) 4, 8, 12 B) 5, 10, 15
C) 10, 20, 30 D) 12, 24, 36
 
Answer & Explanation Answer: D) 12, 24, 36

Explanation:

Let the required numbers be x, 2x, 3x.   Then, their H.C.F =x. so, x= 12

Therefore, The numbers are 12, 24, 36

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Filed Under: HCF and LCM

Q:

Which of the following has most number of divisors?

A) 99 B) 101
C) 176 D) 182
 
Answer & Explanation Answer: C) 176

Explanation:

99  = 1 x 3 x 3 x 11

101= 1 x 101

176= 1 x 2x 2 x 2 x 2 x 11

182= 1 x 2 x 7 x 13

So, divisors of 99 are 1, 3, 9, 11, 33, 99

      divisors of 101 are 1,101

      divisors of 176 are 1, 2, 4, 8, 16, 22, 44, 88, 176

      divisors of 182 are 1, 2, 7, 13, 14, 26, 91, 182

Hence , 176 hasthe most number of divisors. 

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Filed Under: HCF and LCM

Q:

A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?

A) 75 B) 82
C) 100 D) 110
 
Answer & Explanation Answer: D) 110

Explanation:

Originally let there be x men.

Less men, More days     (Indirect Proportion)

 Therefore, (x-10) : x  :: 100 :110

=> (x - 10) * 110 = x * 100    => x= 110

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Filed Under: Chain Rule

Q:

In a public bathroom there are n taps 1,2,3...n. Tap1 and Tap2 take equal time to fill the tank while Tap3 takes half the time taken by Tap2 and Tap4 takes half the time taken by Tap3. Similarly each next number of tap takes half the time taken by previous number of Tap i.e, K-th Tap takes half the time taken by (K-1)th Tap. If the 10th tap takes 2 hours to fill the tank alone then what is the ratio of  efficiency of 8th tap and 12th tap, respectively?

A) 4:1 B) 5:3
C) 16:1 D) 1:16
 
Answer & Explanation Answer: D) 1:16

Explanation:

Time taken by 8th tap = 2 x 2 x 2= 8 hours

Time taken by 12th tap = 2x (1/2) x (1/2)  = 1/2 hour

Ratio of time taken by 8th tap and 12th tap = 8 : 1/2 =16:1

Therefore, Ratio of efficiencies of 8th tap and 12th tap =1:16

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Filed Under: Time and Work

Q:

Mr. stenley employed a certain number of typist for his project. 8 days later 20% of the typist left the job and it was found that it took as much time to complete the rest work from then as the entire work needed with all the employed typists. The average speed of a typist is 20 pages/hour. Minimum how many typist could be employed? 

A) 10 B) 5
C) 15 D) 4
 
Answer & Explanation Answer: B) 5

Explanation:

Since 20% i.e 1/5 typists left the job. So, there can be any value which is multiple of 5 i.e, whose 20% is always an integer. Hence, 5 is the least possible value.

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Filed Under: Time and Work

Q:

A Contractor employed a certain number of workers  to finish constructing a road in a certain scheduled time. Sometime later, when a part of work had been completed, he realised that the work would get delayed by three-fourth of the  scheduled time, so he at once doubled the no of workers and thus he managed to finish the road on the scheduled time. How much work he had been completed, before increasing the number of workers?

A) 10 % B) 14 ( 2/7 )%
C) 20 % D) Can't be determined
 
Answer & Explanation Answer: B) 14 ( 2/7 )%

Explanation:

Let he initially employed x workers which works for D days and he estimated 100 days for the whole work and then he doubled the worker for (100-D) days.

D * x +(100- D) * 2x= 175x 

=>  D= 25 days 

Now , the work done in 25 days = 25x 

Total work = 175x

Therefore, workdone before increasing the no of workers = 25x175x×100 % = 1427%

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Filed Under: Time and Work

Q:

The ratio of efficiency of A is to C is 5:3. The ratio of number of days taken by B is to C is 2:3. A takes 6 days less than C, when A and C completes the work individually. B and C started the work and left after 2 days. The number of days taken by A to finish the remaining work is:

A) 4.5 B) 5
C) 6 D) 9 1/3
 
Answer & Explanation Answer: C) 6

Explanation:

                       A   :   C    

 

Efficiency      5    :   3    

 

No of days   3x   :  5x     

 

Given that, 5x-6 =3x  => x = 3  

 

Number of days taken by A = 9  

 

Number of days taken by C = 15     

 

 

 

           B  :  C    

 

Days   2  :  3  

 

Therefore, Number of days taken by B = 10   

 

Work done by B and C in initial 2 days = 2110+115= 1/3  

 

Thus,  Rest work =2/3  

 

Number of days required by A to finish 2/3 work = (2/3) x 9 = 6 days

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Filed Under: Time and Work

Q:

A is thrice efficient as B and C is twice as efficient as B. what is the ratio of number of days taken by A,B and C, when they work individually?

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

Explanation:

                                                A    :    B    :    C   

Ratio of efficiency               3     :    1    :    2   

Ratio of No.of days            1/3  :   1/1  :   1/2    

     or                                       2    :    6    :    3   

Hence A is correct.  

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Filed Under: Time and Work