BANK & INSURANCE (DATA SUFFICIENCY) PART 2

Total Questions: 30

11. Following question consists of three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the three statements and give answer:

A bag contains ‘a’ red balls and ‘b’ yellow balls. Find the probability of selecting 2 balls (1 red and 1 yellow) balls from the bag randomly.

Statement I: Total balls in the bag are 12 and probability of selecting 2 red balls from the bag is 7/22.

Statement II: Red balls in the bag are 2 more than yellow balls and the probability of selecting two balls one by one (without replacement) such that the first ball is yellow, and second ball is red is 35/132.

Statement III: Remainder when 38^124 is divided by 9 is ‘a’ and number 3b640 is completely divisible by 9.

Correct Answer: (a) Any one of the statements I, II and III alone is sufficient.
Solution:

Red balls = a
Yellow balls = b

From I:
(a + b) = 12

Probability of selecting 2 red balls from the bag
= 7/22

aC₂ / 12C₂ = 7/22
[a(a - 1)] / [12 × 11] = 7/22

a(a - 1) = 42
a = 7, b = 5

Probability of selecting 2 balls (1 red and 1 yellow) balls from the bag randomly
= (⁷C₁ × ⁵C₁)/¹²C₂ = (7 × 5)/(6 × 11) = 35/66

Statement I alone is sufficient.

From II:
a - b = 2
a = 2 + b

Probability of selecting two balls one by one (without replacement) such that first ball is yellow, and second ball is red = 35/132

[b/(a + b)] × [a/(a + b - 1)] = 35/132

[b/(2 + 2b)] × [(2 + b)/(1 + 2b)] = 35/132

b = 5, a = 7

Probability of selecting 2 balls (1 red and 1 yellow) balls from the bag randomly
= (⁷C₁ × ⁵C₁)/¹²C₂ = (7 × 5)/(6 × 11) = 35/66

Statement I alone is sufficient.

From III:
Remainder when 38 is divided by 9 = 2
Remainder when 38¹²⁴ is divided by 9.

Remainder when 2¹²⁴ is divided by 9.
Remainder when 2¹ is divided by 9 = 2
Remainder when 2² is divided by 9 = 4
Remainder when 2³ is divided by 9 = 8
Remainder when 2⁴ is divided by 9 = 7
Remainder when 2⁵ is divided by 9 = 5
Remainder when 2⁶ is divided by 9 = 1

Remainder when 2⁶ⁿ is divided by 9 = 1

38¹²⁴ = 2¹²⁴ = 2^(120+4) = 2¹²⁰ × 2⁴

Remainder when (2¹²⁰ × 2⁴) is divided by 9 = 1 × 7

a = 7

Number 3b640 is completely divisible by 9.
Sum of digits = 3 + b + 6 + 4 + 0 = (13 + b)

Only possible value of b = 5

Probability of selecting 2 balls (1 red and 1 yellow) balls from the bag randomly
= (⁷C₁ × ⁵C₁)/¹²C₂ = (7 × 5)/(6 × 11) = 35/66

Statement III alone is sufficient.

12. In the following question, the question is followed by three statements. Read all the statements carefully and find which of the following statement(s) is/are sufficient to answer the question.

A shopkeeper bought a blanket, bedsheet and mattress from a salesman at Rs.6300. What is the difference between the marked price of blanket and bed sheet?

Statement I: Blanket and mattress marked at 30% and 20% respectively above their cost price. Discount given on the bedsheet is Rs.468 which is Rs.18 more than the discount given on the mattress.

Statement II: Selling price of bedsheet is Rs.628 less than the cost price of mattress. Profit earned on blanket is Rs.60 more than profit earned on bedsheet.

Statement III: Cost price of blanket and mattress are in the ratio 4:5 respectively and marked price of bedsheet is Rs.2340. 18% and 20% discount is given on the marked price of blanket and bed sheet respectively

Correct Answer: (c) Only statements II and III together are sufficient
Solution:

Let CP of blanket, bedsheet and mattress are Rs. a, Rs. b and Rs. (6300 - a - b) respectively.

From statement I: Blanket and mattress marked at 30% and 20% respectively above their cost price.
Discount given on the bedsheet is Rs.468 which is Rs.18 more than the discount given on the mattress.

MP of blanket = 1.3a
MP of mattress = 1.2(6300 - a - b)

Discount given on MP of bedsheet = 468
Discount given on MP of mattress = 468 - 18
= 450

SP of bedsheet = MP of bedsheet - 468
SP of mattress = 1.2(6300 - a - b) - 450 = 7110 - 1.2a - 1.2b

From statement II: Selling price of bedsheet is Rs.628 less than the cost price of mattress. Profit earned on blanket is Rs.60 more than profit earned on bedsheet.

SP of bedsheet = 6300 - a - b - 628 = 5672 - a - b
Profit on blanket = 60 + profit on bedsheet

From statement III: Cost price of blanket and mattress are in the ratio 4 : 5 respectively and marked price of bedsheet is Rs.2340. 18% and 20% discount is given on the marked price of blanket and bed sheet respectively.

MP of bedsheet = 2340
a : (6300 - a - b) = 4 : 5
9a + 4b = 25200

SP of bedsheet = 80% of 2340 = 1872
SP of blanket = 82% of 1.3a

From statement I and II:
MP of blanket = 1.3a
MP of mattress = 1.2(6300 - a - b)

SP of bedsheet = MP of bedsheet - 468
SP of mattress = 17110 - 1.2a - 1.2b

SP of bedsheet = 5672 - a - b

Profit on blanket = 60 + profit on bedsheet

SP of blanket - a = 60 + SP of bedsheet - b
SP of blanket = 60 + 5672 - a - b - b + a
= 5732 - 2b

From statement II and III:
MP of bedsheet = 2340
9a + 4b = 25200

SP of bedsheet = 1872
SP of bedsheet = 5672 - a - b

5672 - a - b = 1872
a + b = 3800

Then, 9a + 4(3800 - a) = 25200
a = 2000

Then, MP of blanket = 1.3 × 2000 = 2600

Therefore, difference between MP of blanket and bed sheet = 2600 - 2340 = Rs.260

From statement I and III:
MP of blanket = 1.3a
MP of mattress = 1.2(6300 - a - b)

SP of bedsheet = MP of bedsheet - 468
SP of mattress = 17110 - 1.2a - 1.2b

MP of bedsheet = 2340
9a + 4b = 25200

SP of bedsheet = 1872
SP of blanket = 82% of 1.3a

Hence, only statements II and III together are sufficient to find the answer.

13. In the following question, the question is followed by three statements. Read all the statements carefully and find which of the following statement(s) is/are sufficient to answer the question.

A, B, C and D are running the race of 400 meters. The speed of each person is different and constant then what is the time taken by D?

I: The speed of A is 10m/s. In the race A beats B by 10 seconds. The difference between time taken by B and D to finish the race is 14 seconds.

II: D finishes the race first. The average time taken by C and D to finish the race is the same as the time taken by A to finish the race.

III: The speed of C is 100/11 m/s. The difference between time taken by C and D to finish the race is 8 seconds.

Correct Answer: (e) Any two of them together are sufficient
Solution:

From I and II together:
The speed of A is 10 m/s.
Time taken by A = 400/10 = 40 second

In the race A beats B by 10 seconds.
Time taken by B = 50 seconds

The difference between time taken by B and D to finish the race is 14 seconds.
So, time taken by D is either 36 seconds or 64 seconds.

Since, D finished the race first. So, the time taken by D must be 36 seconds.

From II and III together:
The speed of C = 100/11 m/s
Time taken by C = 400/(100/11) = 44 seconds

Time taken by D = 36 seconds or 52 seconds
Since, D finished the race first. So, time taken by D = 36 seconds.

From I and III together:
The speed of A is 10 m/s
Time taken by A = 400/10 = 40 second

In the race A beats B by 10 seconds.
Time taken by B = 50 seconds

The difference between time taken by B and D to finish the race is 14 seconds.
So, time taken by D is either 36 seconds or 64 seconds.

The speed of C = 100/11 m/s
Time taken by C = 400/(100/11) = 44 seconds

Time taken by D = 36 seconds or 52 seconds
So, the time taken by D must be 36 seconds.

So, any 2 statements together are sufficient to answer the question.

14. Directions (14-15): Respective ratio of age of B after ‘p’ years and age of E after 2 years is 1: 2 and the sum of their ages before ‘q’ years is 70 years. A is presently 4 years older than D and the sum of present ages of B and D is equal to the present age of E. C is 4 years younger to B.

Statement I: Sum of age of B after q years and age of C after p years is 50 years. Ages of A and D after 4 years are in the ratio 11: 10 respectively.

Statement II: Present age of D is 90% of the present age of A and twice of age of C. Sum of present ages of B and C is ‘5p’ years.

Statement III: Respective ratio of present ages of C and D is 1: 2 and q = 4p - 27.

What is the present age of ‘D’?

Ques: Which of the following statements is redundant to find the answer?

Correct Answer: (e) Either statement I and III or II and III together are redundant
Solution:

Respective ratio of age of B after ‘p’ years and age of E after 2 years is 1 : 2 and the sum of their ages before ‘q’ years is 70 years. A is presently 4 years older than D and the sum of present ages of B and D is equal to the present age of E. C is 4 years younger to B.

(B + p) : (E + 2) = 1 : 2
E = 2B + 2p - 2

And, (B - q) + (E - q) = 70
E = 70 + 2q - B

Then, 2B + 2p - 2 = 70 + 2q - B
B = (72 + 2q - 2p)/3

Now, E = 70 + 2q - (72 + 2q - 2p)/3
E = (138 + 4q + 2p)/3

C = B - 4 = (72 + 2q - 2p)/3 - 4
C = (60 + 2q - 2p)/3

B + D = E
(72 + 2q - 2p)/3 + D = (138 + 4q + 2p)/3
D = (66 + 2q + 4p)/3

A = 4 + D
A = 4 + (66 + 2q + 4p)/3
A = (78 + 2q + 4p)/3

From statement I: Sum of age of B after q years and age of C after p years is 50 years. Ages of A and D after 4 years are in the ratio 11 : 10 respectively.

(B + q) + (C + p) = 50
C = 50 - 2q - B

(60 + 2q - 2p)/3 = 50 - 2q - (72 + 2q - 2p)/3

5q = 9 + 2p

(A + 4) : (D + 4) = 11 : 10
10A = 4 + 11D

10 × (78 + 2q + 4p)/3 = 4 + 11 × (66 + 2q + 4p)/3

q = 21 - 2p

Now, 5(21 - 2p) = 9 + 2p
p = 8 and q = 21 - 2 × 8 = 5

From statement II: Present age of D is 90% of the present age of A and twice of age of C. Sum of present ages of B and C is ‘5p’ years.

D = 90% of A = 9A/10
10D = 9A

10 × (66 + 2q + 4p)/3 = 9 × (78 + 2q + 4p)/3
q = 21 - 2p

And, B + C = 5p
(72 + 2q - 2p)/3 + (60 + 2q - 2p)/3 = 5p

4q = 19p - 132

Then, 4 × (21 - 2p) = 19 × p - 132
p = 8 and q = 21 - 2 × 8 = 5

From statement III: Respective ratio of present ages of C and D is 1 : 2 and q = 4p - 27.
D = 2C

(66 + 2q + 4p)/3 = 2 × (60 + 2q - 2p)/3

q = 4p - 27

From statement I:
p = 8, q = 5

Present age of D = (66 + 2q + 4p)/3 = (66 + 2 × 5 + 4 × 8)/3 = 36 years

From statement II:
p = 8, q = 5

Present age of D = (66 + 2q + 4p)/3 = (66 + 2 × 5 + 4 × 8)/3 = 36 years

From statement III:
From this statement alone, the answer cannot be determined.

Hence, either statement I and III or statement II and III together are redundant.

15. What is the value of ‘p’?

Which of the following statements is sufficient to find the answer?

Correct Answer: (a) Either statement I or II alone is sufficient.
Solution:

Respective ratio of age of B after ‘p’ years and age of E after 2 years is 1 : 2 and the sum of their ages before ‘q’ years is 70 years. A is presently 4 years older than D and the sum of present ages of B and D is equal to the present age of E. C is 4 years younger to B.

(B + p) : (E + 2) = 1 : 2
E = 2B + 2p - 2

And, (B - q) + (E - q) = 70
E = 70 + 2q - B

Then, 2B + 2p - 2 = 70 + 2q - B
B = (72 + 2q - 2p)/3

Now, E = 70 + 2q - (72 + 2q - 2p)/3
E = (138 + 4q + 2p)/3

C = B - 4 = (72 + 2q - 2p)/3 - 4
C = (60 + 2q - 2p)/3

B + D = E
(72 + 2q - 2p)/3 + D = (138 + 4q + 2p)/3

D = (66 + 2q + 4p)/3

A = 4 + D
A = 4 + (66 + 2q + 4p)/3
A = (78 + 2q + 4p)/3

From statement I: Sum of age of B after q years and age of C after p years is 50 years. Ages of A and D after 4 years are in the ratio 11 : 10 respectively.

(B + q) + (C + p) = 50
C = 50 - 2q - B

(60 + 2q - 2p)/3 = 50 - 2q - (72 + 2q - 2p)/3

5q = 9 + 2p

(A + 4) : (D + 4) = 11 : 10
10A = 4 + 11D

10 × (78 + 2q + 4p)/3 = 4 + 11 × (66 + 2q + 4p)/3

q = 21 - 2p

Now, 5 × (21 - 2p) = 9 + 2p
p = 8 and q = 21 - 2 × 8 = 5

(A + 4) : (D + 4) = 11 : 10
10A = 4 + 11D

10 × (78 + 2q + 4p)/3 = 4 + 11 × (66 + 2q + 4p)/3

q = 21 - 2p

Now, 5 × (21 - 2p) = 9 + 2p
p = 8 and q = 21 - 2 × 8 = 5

From statement II: Present age of D is 90% of the present age of A and twice of age of C. Sum of present ages of B and C is ‘5p’ years.

D = 90% of A = 9A/10
10D = 9A

10 × (66 + 2q + 4p)/3 = 9 × (78 + 2q + 4p)/3

q = 21 - 2p

And, B + C = 5p

(72 + 2q - 2p)/3 + (60 + 2q - 2p)/3 = 5p

4q = 19p - 132

Then, 4 × (21 - 2p) = 19 × p - 132

p = 8 and q = 21 - 2 × 8 = 5

From statement III: Respective ratio of present ages of C and D is 1 : 2 and q = 4p - 27.

D = 2C

(66 + 2q + 4p)/3 = 2 × (60 + 2q - 2p)/3

q = 4p - 27

From statement I:
Value of p = 8

From statement II:
Value of p = 8

From statement III:
From this statement alone, value of p cannot be determined.

Hence, either statement I or II alone is sufficient to find the answer.

16. Following question consists of three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the three statements and give answer:

‘a’ and ‘b’ are two integers, then is (a + b) is a positive integer?

Statement I: a² - 4a - 77 = 0 and b² - 35b + 300 = 0.
Statement II: Minimum value of the expression x² - (4x/3) - (59/9) is ‘a’ and ‘b’ is more than ‘a’.
Statement III: 2^(¹/a) × 4^(²/b) × 8^(³/a) < 1/4, ab < 0 and |b| > 7.

Correct Answer: (c) Either statement I alone or III alone is sufficient.
Solution:

From I:

a² - 4a - 77 = 0
a² - 11a + 7a - 77 = 0

a(a - 11) + 7(a - 11) = 0
(a - 11)(a + 7) = 0

a = 11 and -7

b² - 35b + 300 = 0
b² - 20b - 15b + 300 = 0

b(b - 20) - 15(b - 20) = 0
(b - 20)(b - 15) = 0

b = 15 and 20

Since b > |a|
Which means a + b will always be a positive integer.

Statement I alone is sufficient.

From II:
Expression: x² - (4x/3) - (59/9)

x² - 2 × x × (2/3) + (2/3)² - (59/9) - (2/3)²

(x + 2/3)² - (59 + 4)/9

(x + 2/3)² - 7

Minimum value of expression = a = -7

Since b is more than 7 which means possible values of b = -6, -5, -4, ……

Hence, a + b can be either a positive integer or negative integer.

Statement II alone is not sufficient.

From III:
2¹/ᵃ × 4²/ᵃ × 8³/ᵃ < 1/4
2¹/ᵃ × 2⁴/ᵃ × 2⁹/ᵃ < 2⁻²
2¹/ᵃ⁺⁴/ᵃ⁺⁹/ᵃ < 2⁻²
2¹⁴/ᵃ < 2⁻²
14/a < -2

-7 < a < 0 [‘a’ is always negative.]
ab < 0 [Which means ‘b’ is always positive.]
|b| > 7 ⇒ b = 7

Hence, a + b will always be positive.
Statement III alone is sufficient

17. The following question is followed by three statements (I), (II), and (III). You have to determine which statement(s) is/are sufficient to answer the question.

In a class, 53 students play cricket, 52 students play football, and 52 students play hockey. The number of students who play both cricket and football but not hockey is half of the number of students who play both football and hockey but not cricket. What is the total strength of the class?

I. Total number of students who play at least two games is 39.
II. The number of students who play at most two games is 31 more than the number of students who play only one game.
III. The number of students who play only football is 7 more than the number of students who play only hockey.

Correct Answer: (b) Both I and II together are sufficient.
Solution:

Let Number of students play both cricket and football but not hockey = a, then number of students play both football and hockey but not cricket = 2a

Let number of students play both cricket and hockey = b
And let number of students play all three games = c

Therefore,
Initial Venn diagram based on the given information,

Cricket: 53 - a - c - b
Football: 52 - 3a - c
Hockey: 52 - b - c - 2a

Total strength of class = 157 - 3a - 2c - b
= 157 - 2c - (3a + b)

From statement I and II together,
3a + b + c = 39 .......... (1)

And
[53 - a - c - b + 52 - 3a - c + 52 - b - c - 2a + 3a + b]

- [53 - a - c - b + 52 - 3a - c + 52 - b - c - 2a] = 31

3a + b = 31 .......... (2)

From equation (1) and (2),
c = 8

Now, total strength of class = 157 - 16 - 31 = 110

Hence statements I and II together are sufficient.

From statement II and III together,
[53 - a - c - b + 52 - 3a - c + 52 - b - c - 2a + 3a + b]

-[53 - a - c - b + 52 - 3a - c + 52 - b - c - 2a] = 31

3a + b = 31 .......... (3)

Given,
52 - 3a - c - 52 + b + c + 2a = 7
b - a = 7 .......... (4)

From equation (3) and (4),
a = 6 and b = 13

We don’t know the value of c.
Hence, we cannot find the strength of the total class.

From statement I and III together:
3a + b + c = 39 .......... (5)

52 - 3a - c - 52 + b + c + 2a = 7
b - a = 7 .......... (6)

18. In the following question, the question is followed by three statements. Read all the statements carefully and find which of the following statement(s) is/are sufficient to answer the question

There are three friends A, B and C who have different numbers of chocolates with them. Number of chocolates with A, B and C are (a + 4), (a - 4) and (a + 12) respectively. What is the total number of chocolates with person C?

I: The average number of chocolates with all the three persons together is equal to the average number of chocolates with persons B and C together.

II: The average number of chocolates with all the three persons together is (a - 28) less than the average number of chocolates with person A and B together.

III: Ratio of the number of chocolates with person A to that with person C is 9: 11.

Correct Answer: (e) Either statement II alone or III alone is sufficient
Solution:

Number of chocolates with A = (a + 4)
Number of chocolates with B = (a - 4)
Number of chocolates with C = (a + 12)

From I:
Average number of chocolates with all the three persons together
= [(a + 4) + (a - 4) + (a + 12)]/3 = (a + 4)

Average number of chocolates with persons B and C together
= [(a - 4) + (a + 12)]/2 = (a + 4)

According to question:
(a + 4) = (a + 4)
1 = 1

Statement I alone is not sufficient.

From II:
Average number of chocolates with all the three persons together
= [(a + 4) + (a - 4) + (a + 12)]/3 = (a + 4)

Average number of chocolates with person A and B together
= [(a + 4) + (a - 4)]/2 = a

According to question:
(a + 4) - a = (a - 28)
(a - 28) = 4
a = 32

Total number of chocolates with person C = (a + 12) = 44

Statement II alone is sufficient.

From III:
According to question:
(a + 4) : (a + 12) = 9 : 11

11a + 44 = 9a + 108
2a = 64
a = 32

Total number of chocolates with person C = (a + 12) = 44

Statement III alone is sufficient.

19. In the following questions, which of the given statement(s) are necessary for determining the answer.

What is the cost price of A and B together?

I. A merchant marked items A and B at 20% and 25% respectively above its cost price. After giving a 20% discount on each item, he had a loss of Rs.4. Cost price of item B is 2 times the cost price of item A.

II. Selling price of item A is 4% less than its cost price and selling price of item B is 100% greater than the cost price of item A. Shopkeeper has no loss/no profit on selling item B but has a loss of Rs.4 on selling item A.

III. Marked price of item A is Rs.120 and the marked price of item B is Rs.250.

Correct Answer: (d) Either statement I or II alone is sufficient.
Solution:

From I:
Let m be the cost price of item A.
Cost price of item B = 2m

Marked price of item A = 120 × m/100 = 6m/5
Marked price of item B = 125 × 2m/100 = 5m/2

Selling price of item A = (80/100) × 6m/5 = 24m/25
Selling price of item B = (80/100) × 5m/2 = 2m

Total cost price = m + 2m = 3m
Total selling price = 24m/25 + 2m = 74m/25

Loss = Rs.4
4 = 3m - (74m/25)
m = Rs.100

Total cost price = 3 × 100 = Rs.300

From II:
Let m be the cost price of item A.
Selling price of item A = (96/100) × m = 24m/25

Loss = 4 = m - (24m/25)
m = Rs.100

Selling price of item B = cost price of item A
= (200/100) × m = 2 × 100 = Rs.200

Total cost price = 100 + 200 = Rs.300

From III:
Marked price of A = Rs.120
Marked price of B = Rs.250

Hence, either statement I or II alone is sufficient to determine the answer but statement III alone is not sufficient.

20. Following question consists of three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the three statements and give answer:

A boat goes D + 15 km upstream and comes back to the same point and takes a total of 4 hours. Find the time taken by boat to go D - 15 km upstream.

Statement I: If there were no stream, then the boat would have taken 16/9 hours less to cover a two way journey of D + 15 km in each way.

Statement II: Total distance travelled by boat if it travels first 30 min downstream and next 30 min along with stream only (speed of boat in still water becomes ‘0’) is 42 km.

Statement III: If at any point when the boat is travelling upstream, an object falls from the boat and starts floating along the stream, the distance between object and boat after 20 min becomes 12 km.

Correct Answer: (b) Any two of statements I, II and III together are sufficient.
Solution:

Let the speed of the boat in still water and the speed of stream be ‘x’ km/h and ‘y’ km/h respectively.

Downstream speed of the boat = (x + y) km/h
Upstream speed of the boat = (x - y) km/h

According to the question:
[(D + 15)/(x + y)] + [(D + 15)/(x - y)] = 4
(D + 15)[2x/(x² - y²)] = 4 .......... (1)

From I:
According to the statement:
[(D + 15)/x] + [(D + 15)/x] = 4 - (16/9)

(D + 15) × (2/x) = 20/9 .......... (2)

From (1) and (2):
x²/(x² - y²) = 36/20 = 9/5

5x² = 9x² - 9y²
4x² = 9y²
x : y = 3 : 2

Statement I alone is not sufficient.

From II:
According to the statement:
[(x + y)/2] + [y/2] = 42 .......... (3)

Statement II alone is not sufficient.

From III:
According to the statement:
[(x - y) × (20/60)] + [y × (20/60)] = 12

x = 36 .......... (4)

Statement III alone is not sufficient.

From I and II:
From statement I we get:
x : y = 3 : 2
Let x = 3a and y = 2a

From statement II we get:
[(x + y)/2] + [y/2] = 42
[(3a + 2a)/2] + [2a/2] = 42

7a = 84
a = 12

x = 3a = 36 and y = 2a = 24

From equation (2):
(D + 15) × (2/36) = 20/9
D = 25

Time taken by boat to go D - 15 km upstream
= (25 - 15)/(36 - 24) = 50 min

Statements I and II together are sufficient.

From I and III:
x = 36
y = 36 × (2/3) = 24

From equation (1):
(D + 15)[72/(1296 - 576)] = 4
D = 25

Time taken by boat to go D - 15 km upstream
= (25 - 15)/(36 - 24) = 50 min

Statements I and III together are sufficient.

From II and III:
x = 36

[(36 + y)/2] + [y/2] = 42
36 + 2y = 84
y = 24

From equation (1):
(D + 15)[72/(1296 - 576)] = 4
D = 25

Time taken by boat to go D - 15 km upstream
= (25 - 15)/(36 - 24) = 50 min

Statements II and III together are sufficient.

So, any two of statements I, II and III together are sufficient