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Q:

In a bag, there are 8 red, 7 blue and 6 green flowers. One of the flower is picked up randomly. What is the probability that it is neither red nor green ?

$A) \frac{1}{3}$

$B) \frac{8}{21}$

$C) \frac{6}{21}$

$D) \frac{20}{21}$

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

Answer & Explanation Answer: A) Option A

Explanation:

Total number of flowers = (8+7+6) = 21.

Let E = event that the flower drawn is neither red nor green.

= event taht the flower drawn is blue.

--> n(E)= 7

--> P(E)= $\frac{7}{21}$ = $\frac{1}{3}$

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Q:

A box contains 5 green, 4 yellow and 5 white pearls. Four pearls are drawn at random. What is the probability that they are not of the same colour ?

A) 11/91

B) 4/11

C) 1/11

D) 90/91

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

Answer & Explanation Answer: D) Option D

Explanation:

Let S be the sample space. Then,
n(s) = number of ways of drawing 4 pearls out of 14

= $C_{4}^{14}$ ways = $\frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1}$ = 1001

Let E be the event of drawing 4 pearls of the same colour.
Then, E = event of drawing (4 pearls out of 5) or (4 pearls out of 4) or (4 pearls out of 5)

$\Rightarrow C_{1}^{5} + C_{4}^{4} + C_{1}^{5}$ = 5+1+5 =11

P(E) = $\frac{n (E)}{n (S)} = \frac{11}{1001} = \frac{1}{91}$

Required probability = $1 - \frac{1}{91} = \frac{90}{91}$

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Q:

Twenty men can do a work in eighteen days. Eighteen women can complete the same work in fifteen days. What is the ratio between the capacity of a woman and a man ?

A) 4:5	B) 3:4
C) 4:3	D) 2:3

Answer & Explanation Answer: C) 4:3

Explanation:

(20 x 18) men can complete the work in in one day.

one man's one day work = 1/360

(18 x 15) women can complete the work in 1 day

1 woman's one day work = 1/270

So, required ratio = $\frac{1}{270} : \frac{1}{360}$ = 4:3

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Filed Under: Time and Work
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Q:

K can finish the work in 18 days and L can do the same work in 15 days. L worked for 10 days and left the job. In how many days, K alone can finish the remaining work ?

A) 5.5 days	B) 6 days
C) 4.2 days	D) 5 days

Answer & Explanation Answer: B) 6 days

Explanation:

L's 10 days work = $(\frac{1}{15} \times 10) = \frac{2}{3}$

Remaining work = $(1 - \frac{2}{3}) = \frac{1}{3}$

Now, work is done by K in one day = 1/18

1/3 work is done by K in $(18 \times \frac{1}{3})$ = 6 days

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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) $3 \frac{4}{49} d a y s$

B) $12 \frac{4}{49} d a y s$

C) $4 \frac{3}{49} d a y s$

D) $4 \frac{12}{49} d a y s$

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

Answer & Explanation Answer: C) Option C

Explanation:

Raghu can complete the work in (12 x 9)hrs = 108 hrs.

Arun can complete the work in (8 x 11)hrs = 88 hrs.

Raghu's 1 hrs work = 1/108 and Arun's 1 hrs work = 1/88

(Raghu + Arun)'s 1 hrs work = $(\frac{1}{108} + \frac{1}{88}) = \frac{49}{2376}$

So, both Raghu and Arun will finish the work in $\frac{2376}{49} h r s$

Number of days of 12 hours each= $(\frac{2376}{49} \times \frac{1}{12})$ = $\frac{198}{49} = 4 \frac{3}{49} d a y s$

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Q:

P and Q can do a work in 4 hours and 12 hours respectively. P starts the work at 9am and they work alternately for one hour each. When will the work be completed ?

A) 3 am	B) 12 pm
C) 1 pm	D) 3 pm

Answer & Explanation Answer: D) 3 pm

Explanation:

Work done by P and Q in the first two hours, working alternately

= First hour P + Second hour Q

$\Rightarrow \frac{1}{4} + \frac{1}{12} = \frac{1}{3}$

work is completed in 2 hours

Then, the total time required to complete the work by P and Q working alternately=2 x 3= 6hours

Thus, work will be completed at 3pm.

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Q:

K is 4 times as fast as L and working together, they can complete a work in 24 days. In how many days can L alone complete the work ?

A) 30 days	B) 40 days
C) 120 days	D) 80 days

Answer & Explanation Answer: A) 30 days

Explanation:

Given K=4L

-->K+L = 4L+L = 5L

These 5L people can complete the work in 24 days, which means L alone can do the work in (24 x 5)=120 days.

Hence, K alone can do the work in 120/4= 30 days.

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Filed Under: Time and Work
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Q:

I travel 20 miles towards north and then travel 25 miles eastward. I then travel 40 miles rightwards, then travel 30 miles towards left and then travels 12 miles to the left and finally 20 miles northwards. How far am i pproximately from my original destination and in what direction ?

A) 20 miles towards south	B) 13 miles towards south-west
C) 12 miles towards east	D) 13 miles towards north-east

Answer & Explanation Answer: B) 13 miles towards south-west

Explanation:

k41483341709.jpg image

Using pythagorus rule,

$x^{2} = 12^{2} + 5^{2}$

--> x = 13

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Filed Under: Direction Sense Test
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