# Quant Quiz – Mixed Problems – 19

Hello and welcome to exampundit. Here is a set of Quantitative Aptitude Quiz on Mixed Word Problems for bank exams.

1. An urn consists of 3 black, 4 white and 5 blue marbles. Three marbles are drawn randomly. What is the probability that marbles drawn contains marbles of different colour?

(A) 7/11
(B) 3/8
(C) 7/8
(D) 3/11
(E) none of these

Option:Â D

Explanation:

P(E)=n(e)/n(s)=4C1Ã—3C1Ã—5C1/12C3=3/11

1. 4 boys and 6 girls complete a task in 24 days. If the girls are at least half as efficient as the boys, but not more efficient than the boys, what is the range of the number of days for 6 girls and 2 boys to complete the same task?

(A) 28 to 31 days
(B) 29 to 31 days
(C) 33.6 to 35 days
(D) 30 to 33.6 days
(E) none of these

Option:Â D

Explanation:

4boys and 6girls finish in 24 days.
In one day, 4boys + 6girls =Â 1/24Â of task.
If a girl is half as efficient as boy
4b + 3b =Â 1/24, 7b =Â 1/24, b =Â 1/168
6g + 2b = 3b + 2b = 5b, 5m will takeÂ 1685Â days = 33.6 days
If a girl is as efficient as a man
4b + 6g finish in 24 days.
10b finishÂ 1/24Â of task in a day
6g + 2b = 8b, 8b will takeÂ 240/8Â = 30 days to finish the task.
So, the range = 30 to 33.6 days. The new team will take 30 to 33.6 days to finish the task

1. A cistern of 475 litres is completely filled using pipes A and B, with Pipe A being open for 5 more hours than pipe B. If we are to interchange the operating hours of the two pipes than pipe A would have pumped half the water as much as pipe B, then find the time for which pipe B was open. Also, given that if the two pipes were open simultaneously the tank would fill in 19 hours.

(A) 10hr
(B) 14hr
(C) 20hr
(D) 16hr
(E) none of these

Option:Â D

Explanation:

The 475 litres is filled in 19 hours by the two pipes when they are opened simultaneously.
Therefore, rate of water flow by A and B,
A + B =Â 47519Â = 25 litres/hourâ€¦â€¦â€¦â€¦.(1)
Let pipe B was opened for t hours
Then, pipe A was opened for t + 5 hours
A x (t+5) + B x t = 475
(A + B) x t + 5A = 475
25t + 5A = 475
=> 5t + A = 95
Now, using options
t = 16 => 5 x 16 + A = 95 => A = 15

1. A milkman purchases milk at â‚¹ 20/litre and mixes 4 litres of water in it. By selling the resultant mixture at the rate of â‚¹ 20/litre, he earns a profit of 40%. The amount of mixture he had with him to sell was?

(A) 10l
(B) 8l
(C) 7l
(D) 14l
(E) none of these

Option:Â D

Explanation:Â To earn a profit of 40% at Rs 20/litre,
Cost price =Â 20/1.4=100/7

Therefore,
Milk: Water =Â 100/7:40/7Â = 5:2
So, in 4 litres of water, 10 litres of milk would be required. Resultant mixture = 14 litres

1. IfÂ 66Â years are subtracted from the present age of Anika and the remainder is divided byÂ 1818, then the present age of Radika is obtained. If Radika isÂ 22Â years younger to Daizy whose age isÂ 55Â years, then what is Anika present age?

(A) 70years
(B) 45years
(C) 55years
(D) 60years
(E) 47years

Option:Â D

Explanation:

Present age of DaizyÂ =5years
Let present age of AnikaÂ =x
Then, present age of RadikaÂ =xâˆ’6/18
xâˆ’6/18=3â‡’xâˆ’6=3Ã—18=54â‡’x=54+6=60

1. What would be the compound interest accrued on an amount of â‚¹ 7,400 at the rate of 13.5 percent per annum at the end of two years? (rounded off to two digits after decimal)

(A) â‚¹2112.18
(B) â‚¹2022.75
(C) â‚¹2045.18
(D) â‚¹2132.87
(E) none of these

Option:Â D

Explanation:

CI =7400[(1+13.5/100)Â²-1]

= 7400[1.288225 -1]

= 7400 Ã— 0.288225 = Rs 2132.87

1. A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?

(A) 400%
(B) 4%
(C) 100%
(D) 300%
(E) none of these

Option:Â D

Explanation:

Volume of 4 cm cube = 64cc. When it is cut into 1 cm cube, the volume of each of the cubes = 1cc
Hence, there will be 64 such cubes. Surface area of small cubes = 6(1Â²) = 6 sqcm.
Therefore, the surface area of 64 such cubes = 64 Ã—6 = 384 sqcm.
The surface area of the large cube = 6(4Â²) = 6Ã—16 = 96.
% increase =Â 384-96/96Â = 300%

1. If the diagonal and the area of a rectangle are 25 m and 168 m2, what is the length of the rectangle?

(A) 7m
(B) 17m
(C) 31m
(D) 24m
(E) none of these

Option:Â D

Explanation:

The diagonalÂ dÂ = 25m. and area A = 168 m2.
Let ‘l’ be the length and ‘b’ be the width of the rectangle.
Therefore,Â l2Â +Â b2Â =Â d2. andÂ lbÂ = A
We can therefore write (lÂ +Â b)2Â =Â d2Â + 2A and (lÂ –Â b)2Â =Â d2Â – 2A.
Substituting and solving we get,Â lÂ +Â bÂ = 31 andÂ lÂ –Â bÂ = 17. HenceÂ lÂ = 24 andÂ bÂ = 7

1. The average age of 3 children in a family is 20% of the average age of the father and the eldest child. The total age of the mother and the youngest child is 54. If the fatherâ€™s age is 47 years, what the age of second child?

(A) 22years
(B) 31years
(C) 27years
(D) cannot be determined
(E) none of these

Option:Â D

Regards

Team EP

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