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Data sufficiency
Directions (1 – 3): In each of the following questions, a question is followed by three statements I, II and III. Read all the statements to find the answer to given question and then answer accordingly that which statement/s can give the answer alone/together.
1) What percent of the profit earned by shopkeeper?
Statement I: The shopkeeper sold the mobile is Rs.7500. If he sold it for Rs.300 more, then he earns the profit of 30%.
Statement II: Ratio of the marked to cost price of the mobile is 5:4 and the discount offered and selling price of the mobile is Rs.1000 and Rs.9000 respectively.
Statement III: If the ratio of the marked price to selling price of the mobile is 4: 3 and the discount offered by 20% on the marked price of the mobile.
a) Only I and II are sufficient
b) Only II and III are sufficient
c) Either I alone or II alone sufficient but III not sufficient
d) All I, II and III necessary to the answer the question
e) The question cannot be answered even with all I, II and III
2) In how many days 6 men and 5 women can complete the work working together?
Statement I: The ratio of efficiency of man to woman is 2: 1
Statement II:Â 9 Women can complete the work in 20 days
Statement III:Â 18 men can complete the work in 20 days
a) Only statement A
b) A & B together
c) A & B together or A & C together
d) Any of the two statements together
e) None of the above
3) Find the ratio of the speed of the boat in still water and the speed of the stream?
Statement I: Time taken by the boat to going a certain distance upstream is twice the time taken in rowing the same distance downstream.
Statement II: Boat can row a distance of 24 km in 4 hours in upstream.
Statement III: Speed of the boat in still water is 9 kmph.
a) Only I follow
b) Both II and III follow
c) Only I and III follow
d) Either I or Both II and III together
e) None of follow
Directions (Q. 4 – 5): In each of the following questions, a question is followed by two statements Iand II. Read all the statements to find the answer to given question and then answer accordingly that which statement/s can give the answer alone/together.
4) What is the marked price of the shirt?
Statement I: A shopkeeper purchases 4 shirts for Rs. 5740 and makes a total profit of Rs. 176 on selling all 4 shirts together. A discount of 13% is given on each shirt.
Statement II: A shopkeeper marks the price at 26% more than the cost price and makes a profit of Rs. 300 after giving some discount.
a) Â The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
b) The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
c) The data either in statement I alone or in statement II alone is sufficient to answer the question
d) The data given in both statements I and II together are necessary to answer the question.
e) The data given in both statements I and II together are not sufficient to answer the question
5) Average present age of Ram, Birbal, Tony and Jitu is 19.5 years. Find the difference between the present ages of Birbal and Jitu.
Statement I: After 10 years, the ratio of age of Ram to Jitu will be 13: 15. Six years ago, the ratio of ages of Birbal to Tony was 3: 2.
Statement II: Average age of Ram and Birbal after 7 years is 27 years. After 18 years, Tony will be 2 years younger than Jitu.
a) Â The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
b) The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
c) The data either in statement I alone or in statement II alone is sufficient to answer the question
d) The data given in both statements I and II together are necessary to answer the question.
e) The data given in both statements I and II together are not sufficient to answer the question
Caselet
Directions (6 – 10): Study the following information carefully and answer the questions given below.
There are four trains named Marudhar Express, Shatabdi Express, Surya Nagri Express and Tejas whose related information are given below-
(i) Speed of Shatabdi Express is 129.6 Km/hr and its length is 136 meter which is 14 meter less than Surya Nagri express and 84 meter less than that of Marudhar express.
(ii) Speed of Marudhar express is 11 1/9 % more than the speed of Shatabdi Express and 66 2/3 % more than the speed of Surya Nagri Express.
(iii)Â Ratio of time taken by Marudhar express and Tejas to reach Jodhpur from Mumbai is 9: 8.
(iv) Length of Tejas is 4 6/11% less than the length of Marudhar express.
6) Find time taken by Surya Nagri express to cross a platform which length is 210 meter?
a) 18 sec
b) 12 sec
c) 15 sec
d) 17 sec
e) None of these
7) If distance between Jodhpur and Mumbai is 720 km and Shatabdi exp. Travelling from jodhpur to Mumbai And Surya Nagri exp. Moving from Mumbai to Jodhpur. Find what time it cross to each other and distance between Jodhpur to meeting point?
a) 3hr 20 minute; 440 km
b) 3hr 20 minute; 432 km
c) 4hr 20 minute; 420 km
d) 5hr 40 minute; 430 km
e) Cannot be determined
8) Find the ratio of time taken by Marudhar Express and Tejas to cross a man who walks in same direction at speed of 18 km/hr?
a) 139: 137
b) 176: 147
c) 122: 123
d) 127: 117
e) None of these
9) Find the difference of time (in hour) taken by Shatabdi Express and Surya Nagri Express to reach Mumbai from Ahmedabad if the total distance between these two cities is 1080 km?
a) 4 hr 10 minute
b) 3 hr 20 minute
c) 2 hr 10 minute
d) 5 hr 25 minute
e) None of these
10) In how much time Tejas and Shatabdi Express will cross each other if they travel in same direction?
a) 37.44 seconds
b) 34.88 seconds
c) 36.74 seconds
d) 38.44 seconds
e) 83.44 seconds
Answers :
Directions (1-5) :
1) Answer: C
From statement I,
SP = 7500
CP * 130/100 = 7500 + 300
CP = 6000
Profit percentage = 7500 – 6000/6000 * 100 = 25%
So, Statement I alone is sufficient to answer the question.
From statement II,
MP = 5x
CP = 4x
5x – 1000 = 9000
5x = 10000
X = 2000
CP = 4 * 2000 = 8000
Profit percentage = 9000 – 8000/8000 * 100 = 12.5%
So, Statement II alone is sufficient to answer the question.
From statement III,
MP = 4x
SP = 3x
4x * 80/100 = 3x
So, Statement III alone is not sufficient to answer the question.
2) Answer: D
Statement I:
The ratio of efficiency of man to woman = 2∶ 1
This statement alone is not sufficient to answer the question.
Statement II:Â
One woman can complete the work in = 1/(20 * 9) = 1/180
One woman can complete the work in 180 days.
This statement alone is not sufficient to answer the question.
Statement III:Â
One man can complete the work in = 1/(20 * 18) = 1/360
One woman can complete the work in 360 days
This statement alone is not sufficient to answer the question.
From statement I and II
9W * 20 = (6M + 5W) * x
= 9 * 1 * 20 = (6 * 2 + 5 * 1) * x
= x = 180/17 days
From these two statements we can find the answer.
From statement II and III
9W * 20 = 18M * 20
M: W = 1: 2
Than
9W * 20 = (6M + 5W) * x
x = 360/16 = 22.5 days
From these two statements we can find the answer.
From statement III and I
18M * 20 = (6M + 5W) * x
x = 18 * 2 * 20/17 = 720/17 days
From these two statements we can find the answer.
Thus any two of these statements are require answering the questions.
3) Answer: D
From statement I,
Given Ratio of time: (x + y): (x – y) = 1: 2
Ratio of speed: (x + y): (x – y) = 2: 1 (2x , x)
Then speed ratio boat and stream = (2x + x)/2: (2x – x)/2 = 3: 1
This statement alone is sufficient to answer the question.
From statement II,
Upstream speed = 24/4 = 6 kmph
This statement alone is not sufficient to answer the question.
From statement II,
Speed of boat =Â 9 kmph
This statement alone is not sufficient to answer the question.
From statement II and III,
Than speed of stream is = x – y = 6
9 – y = 6
y = 3km/hr
Then required ratio = 9: 3 = 3: 1
From these two statements we can find the answer.
Thus either statement I alone or statement II & III together needed to answer the question.
Directions (4-5) :
4) Answer: A
From statement I,
Selling price of all for shirt = 5740 + 176 = 5916
Sp of each shirt = 5916/4 = 1479
M.R.P = 1479/87 x 100 = 1700
This statement alone is sufficient to answer the question.
From statement II,
Let the cost price be 100x
MP = 100x * 126/100 = 126x
Profit = 300
Statement II alone is not sufficient to answer the question
5) Answer: D
Let present age of Ram, Birbal, Tony and jitu is P years, Q years, R years and S years, respectively
Sum of present age of Ram, Birbal, Tony and jitu
= 19.5 * 4 = 78Â years
P + Q + R + S = 78 year
Statement I:
According to the question:
(P + 10)/(S + 10) = 13/15
15P + 150 = 13 S + 130
13 S – 15P = 20
And,    (Q – 6)/(R – 6)  = 3/2
2Q – 12 = 3R – 18
3R – 2Q = 6
So, statement I alone is not sufficient to answer the question.
Statement II:
(P + Q + 14)/2 = 27
P + Q = 54 – 14
P + Q = 40
Also, R = S – 2
Also, R + S =78 – 40
R + S = 38
Solving, both the above equations, we get
R = 18 ; S = 20
Here, we can’t find the value of P and Q
So, statement II alone is not sufficient to answer the question.
Combining statements I and II together,
3R – 2Q = 6
3 * 18 – 2Q = 6
Q = 24
We have to find (Q – S) or (S – Q), which we can find from here.
Thus, the data in both Statements I and II together are necessary to answer the question.
Directions (6 – 10):
Speed of Shatabdi Express = 129.6 Km/hr = 129.6 * 5/18 = 36 m/s
Length of Shatabdi Express = 136 m
Length of Surya Nagri express = 136 + 14 = 150 m
Length of Marudhar express = 136 + 84 = 220 m
Speed of Marudhar express = 129.6 + 129.6 * 100/900 = 144 kmph
= 144 * 5/18 = 40 m/s
Speed of Shatabdi Express = 144 * 5/3 = 86.4 kmph  (66 2/3% = 2/3)
= 86.4 * 5/18 = 24 m/s
Ratio of time taken by Marudhar express and Tejas to reach Jodhpur = 9: 8
Speed ratio of Marudhar express and Tejas = 8: 9
Speed of Tejas = 144/8 * 9 = 162 kmph = 162 * 5/18 = 45 m/s
Length of Tejas = 220 – 220 * 50/1100 = 210  (4 6/11% = 50/11% = 50/1100)
6) Answer: C
Time = (210 + 150)/24 = 15 sec
7) Answer: B
Time = 720/(129.6 + 86.4) = 720/216 = 3hr 20 minute
Distance = 129.6 x 3 +129.6 x 1/3 = 432 km
8) Answer:Â B
Speed of man = 18 km/hr = 5m/s
Relative speed of Marudhar Express = 40 – 5 = 35
Relative speed of Tejas = 45 – 5 = 40
Required answer = 220/35: 210/45 = 176: 147
9) Answer: A
Required difference
= 1080/(86.4) – 1080/(129.6) = 25( 1/2 – 1/3 ) = 4 hr 10 minute
10) Answer: D
Total distance = 210 + 136 = 346
Relative speed = 45 – 36 = 9
Required time = 346/9 = 38.44 seconds
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