## Exim Bank Ltd MTO-2013

### Section 2: Mathematical And Analytical Aptitude

21. In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

A. 30%

B. 70%

C. 100%

D. 250%

E. None of these

Option: B

Explanation:

Let C.P.= Tk.100.

Then, Profit = Tk.320,

S.P.= Tk.420.

New C.P.=125% of Tk.100=Tk.125

New S.P. = Tk. 420.

Profit = Tk.(420 – 125)= Tk.295

∴ Required percentage = (295/420)* 100

70%(approx)

22. What percentage of numbers from 1 to 70 have 1 or 9 in the unit’s digit?

A. 10%

B. 14%

C. 20%

D. 21%

E. None of these

Option: C

Explanation:

Numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.

Number of such number =14

∴ Required percentage = 14/70 x 100 % = 20%.

23. The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

A. 16 cm

B. 18 cm

C. 20 cm

D. 24 cm

E. None of these

Option: B

Explanation:

=> 2l + 2b = 5b

=> 3b = 2l

b=(2/3)l

Then, Area = 216 cm2

=> l x b = 216

=> l x (2/3)l =216

=> l2 = 324

l = 18 cm.

24. The average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

A. 85 kg

B. 80 kg

C. 75 kg

D. Cannot be determined

E. None of these

Option: A

Explanation:

Total weight increased = (8 x 2.5) kg = 20 kg.

Weight of new person = (65 + 20) kg = 85 kg.

25. Mr. Khan invested an amount of Tk. 13,900 divided into two different schemes A and B at a simple interest rate of 14% per annum and 11% per annum respectively. If the total amount of simple interest earned in 2 years be Tk. 3,508, what was the amount invested in Scheme B?

A. Tk. 6400

B. Tk. 6500

C. Tk. 7200

D. Tk. 7500

E. None of these

Option: D

Explanation:

Let the sum invested in Scheme A be TK. x and

that in Scheme B be TK. (13900 – x).

Then, (X*14*2/100)+{(13900-X)*11*2/100} = 3508.

28x/100 + (13900*22)-(x*22)/100 = 3508.

28x/100 + 305800-22x/100 = 3508.

28x+305800-22x/100 = 3508.

Now,

28x+305800-22x=3508*100.

28x-22x=350800-305800.

6x=45000.

x=45000/6.

x=7500.

26. A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then,a + b=?
A. 10

B. 11

C. 12

D. 15

E. None of these

Option: A

Explanation:

Just use the concept of divisibility of 11 and get the answer.

As number is 13b7 is divisible by 11 the difference of alternate digit must be zero or 11, so 1+b = 3+7

or (1+b) – (3+7) = 0.

So you got b = 9.

A+8 = b, a+8 = 9

so a = 1,

hence a+b = 10.

27. How many times are the hands of a clock at right angle in a day?
A. 22

B. 24

C. 44

D. 48

E. None of these

Option: C

Explanation:

In 12 hours, the right angles 22 times.

In 24 hours, the right angles 44 times.

28. The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percentage; increase of the population per year is-
A. 4.7%

B. 5%

C. 6%

D. 8.75%

E. None of these

Option: B

5%

Explanation:

Increase population in 10 years= (262500 – 175000) =87500

Increase population in 1 year = 87500/10 =8750

So, 175000 * X/100=8750

⇒ 175000x/100 =8750

⇒ 175000x =875000

⇒ x = 875000/175000

∴ x = 5

So, the answer is = 5%

29. The difference of two numbers is 1365.0n dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number?
A. 240

B. 270

C. 295

D. 300

E. None of these

Option: B

270

Explanation:

Let, x – y =1365

According to question:

x/y =6+15

x =6y + 15

Now,

6y + 15 – y =1365

⇒ 5y =1350

∴ y = 270

The smallest number is =270 (Ans)

30. A and B started a partnership business I investing some amount in the ratio of 3:5. C joined them after six months with an amount equal to that of 6. In what proportion should the profit at the end of the first; year be distributed among A, B and C?
A. 3 : 5 : 2

B. 3 : 5 : 5

C. 6 : 10 : 5

D. Cannot be determined

E. None of these

Option: C

6 : 10 : 5

Explanation:

Let, initial investment A : B = 3x :5x

According to question

A : B : C =(3x*12) : (5x*12) : (5x*6) = 36 : 60 : 30 = 6 : 10 : 5

31. In an election between two candidates, one got 55% of the total valid votes. 20% of i the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was-
A. 2700

B. 2900

C. 3000

D. 3100

E. None of these

Option: A

2700

Explanation:

Number of valid votes = 80% of 7500 = 6000.

One candidate gets 55% of valid vote= 6000 x (55/100) = 3300

Other candidate gets = (6000 – 3300) = 2700 (Ans)

32. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?
A. 3 hours

B. 3.25 hours

C. 3.45 hours

D. 4 hours

E. None of these

Option: C

3.45 hours

33. Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q’s age?
A. 2 years

B. 5 years

C. 25 years

D. Cannot be determined

E. None of these

Option: D

Cannot be determined

34. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
A. 3

B. 4

C. 6

D. 9

E. None of these

Option: B

4

Explanation:

Let the ten digit =x, and unit digit =y

Now, (10x + y) – (10y + x) =36

⇒ 10x + y – 10y – x =36

⇒ 9x – 9y = 36

⇒ 9(x – y) = 36

⇒ x – y = 36/9

∴ x – y = 4 (Ans)

35. A jogger running at 9 km/hr alongside a railway track is 240 meters ahead of the engine of a 120 meters long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
A. 3.6 sec

B. 18 sec

C. 36 sec

D. 72 sec

E. None of these

Option: C

36 Second

36. In a race of 200m, A can beat B by 31m and C by 18m. In a race of 350m, C will beat B by-
A. 25 m

B. 19.75 m

C. 22.75 m

D. 19 m

E. None of these

Option: A

25 m

37. A automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes.
A. 10%

B. 10.25%

C. 10.75%

D. 11%

E. None of these

Option: B

10.25%

Explanation:

Let the sum be Tk. 100. Then,

Interest for first 6 months = Tk. 100 x 10 x 1/ 100 x 2 = Tk. 5

Interest for last 6 months = Tk. 105 x 10 x 1/ 100 x 2 = Tk. 5.25

So, Total at the end of 1 year = Tk. (100 + 5 + 5.25) = Tk. 110.25

Effective rate = (110.25 – 100) = 10.25% (Ans)

38. A man can row at 5 km/hr in still water. If the velocity of the current is 1 km/hr and it takes him 1 hour to row to a place and come back, how far is the place? [EXIM Bank MTO-2013 : 2013]
A. 2.4 km

B. 3 km

C. 4.5 km

D. 5 km

E. None of these

Option: A

Explanation:

Let the distance is x km

Rate downstream = 5 + 1 = 6 kmph

Rate upstream = 5 – 1 = 4 kmph

then

x/6 + x/4 = 1 [because distance/speed = time]

=> 2x + 3x = 12

=> x = 12/5 = 2.4 km

39. The price of commodity X increases by 40, paisa every year, while the price of commodity Y increases by 15 paisa every year. If in 2001, the price of commodity X was Tk. 4.20 and that of Y was Tk. 6.30, in which year commodity X will cost 40 paisa more than commodity Y?
A. 2010

B. 2011

C. 2012

D. 2013

E. None of these

Option: B

2011

Question 40- 44

On an island there are exactly seven towns: T, U, V, W, X, Y, and Z, All existing and projected roads on the island are two-way and run perfectly straight between one town and the next. All distances by road are distances from the main square of one town to the main square of another town. U is the same distance by road from T, V, and W as Y is from X and Z. The following are all of the currently existing roads and connections by road on the island:

 Road 1 goes from T to V via U Road 2 goes from U directly to W The triangle road goes from X to Y, from Y to Z, and from Z back to X. Any main square reached by two roads is an interchange between them, and there are no other interchanges between roads.

40. Which of the following is a pair of towns connected by two routes by road that have no stretch of road in common?

A. T and U

B. X and Y

C. U and V

D. V and W

E. None of these

Option-A

T and U

41. If a projected road from T to Y is built, then the shortest distance by road from W to X will be the same as the shortest distance by road from Z to –

A. T

B. V

C. U

D. Y

E. None of these

Option-C

U

42. If two projected roads were built, one from T directly to Y, and one from V directly to Z, then each of the following would be a complete list of the towns lying along one of the routes that a traveler going by road from U to X could select except,

A. T, Z

B. T, X

C. T, Y

D. V, Z

E. None of these

Option-A

T,Z

43. Which of the following is a town from which exactly two other towns can be reached by roads?

A. U

B. V

C. W

D. X

E. None of these

Option-D

X

44. It is possible that the, distance by road from X to Y is unequal to the distance by road from-

A. T to U

B. U to V

C. X to Z

D. U to W

E. None of these