Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

মোট প্রশ্ন: ৫৪

পূর্ববর্তীপৃষ্ঠা ৩ এর ৩

৪১

Hasib took a loan of 1400 tk with simple interest for as many years as the rate of interest. If he paid 126 th as interest at the end of the loan period , what was the rate of interest?

ক.

✓ সঠিক উত্তর

খ.

গ.

ঘ.

12%

ব্যাখ্যা

Let rate = R% and time = R years
Then

(\frac{1Unknown node type: br400 \times R \times R}{100})

$(\frac{1400 \times R \times R}{100})$
= 126

\Rightarrow 14 R^{2}

$\Rightarrow 14 R^{2}$ = 126

R^{2}

$R^{2}$ = 9

∴

$∴$ R = 3

বিষয়: গণিতটপিক: সরল ও যৌগিক মুনাফা (Simple & Compound interest)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

Hasib took a loan of 1400 tk with simple interest for as many years as the rate of interest. If he paid 126 th as interest at the end of the loan period , what was the rate of interest?

ক.

✓ সঠিক উত্তর

খ.

গ.

ঘ.

12%

ব্যাখ্যা

Let rate = R% and time = R years
Then

(\frac{1Unknown node type: br400 \times R \times R}{100})

$(\frac{1400 \times R \times R}{100})$
= 126

\Rightarrow 14 R^{2}

$\Rightarrow 14 R^{2}$ = 126

R^{2}

$R^{2}$ = 9

∴

$∴$ R = 3

৪২

A batsman makes a score of 87 runs in the 17th ining and thus increases his average by 3. What is his average after 17th innings?

ক.

খ.

গ.

✓ সঠিক উত্তর

ঘ.

ব্যাখ্যা

Let the average after 17th match is x
then average before 17th match is x – 3
So, 16(x – 3) + 87 = 17x

\Rightarrow

$\Rightarrow$ x = 87 – 48 = 39

বিষয়: গণিতটপিক: শতকরা (Percentage)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

A batsman makes a score of 87 runs in the 17th ining and thus increases his average by 3. What is his average after 17th innings?

ক.

খ.

গ.

✓ সঠিক উত্তর

ঘ.

ব্যাখ্যা

Let the average after 17th match is x
then average before 17th match is x – 3
So, 16(x – 3) + 87 = 17x

\Rightarrow

$\Rightarrow$ x = 87 – 48 = 39

বিষয়: গণিতটপিক: শতকরা (Percentage)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

৪৩

Two student appeared at an examination. One of them secured 9 makes more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are :

ক.

39, 30

খ.

41, 32

গ.

42, 33

✓ সঠিক উত্তর

ঘ.

43,34

ব্যাখ্যা

Let their marks be (x + 9) and x
Then, x + 9 =

\frac{56}{100}

$\frac{56}{100}$ (x + 9 + x)
25(x + 9) = 14 (2x + 9)
3x = 99

∴

$∴$ x = 33
so, their marks are 42 and 33

বিষয়: গণিতরেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

Two student appeared at an examination. One of them secured 9 makes more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are :

ক.

39, 30

খ.

41, 32

গ.

42, 33

✓ সঠিক উত্তর

ঘ.

43,34

ব্যাখ্যা

Let their marks be (x + 9) and x
Then, x + 9 =

\frac{56}{100}

$\frac{56}{100}$ (x + 9 + x)
25(x + 9) = 14 (2x + 9)
3x = 99

∴

$∴$ x = 33
so, their marks are 42 and 33

বিষয়: গণিতরেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

৪৪

A die is rolled twice. What is the probability of getting a sum equal to 9?

ক.

2/3

খ.

2/9

গ.

1/6

ঘ.

1/9

✓ সঠিক উত্তর

ব্যাখ্যা

Total number of out comes possible when a die is rolled = 6
Hence, total number of out comes possible when a die is rolled twice, n(s) = 6

\times

$\times$ 6 = 36
E = Geting a sum of 9 when the two dice fell = {(3,6), (4,5), (5,4), (6,3)}
Hence n (E) = 4
P(E) =

\frac{n (E)}{n Unknown node type: br(S)} = \frac{4}{36} =Unknown node type: br \frac{1}{9}

$\frac{n (E)}{n (S)} = \frac{4}{36} = \frac{1}{9}$

বিষয়: গণিতটপিক: সম্ভাব্যতা (Probability)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

A die is rolled twice. What is the probability of getting a sum equal to 9?

ক.

2/3

খ.

2/9

গ.

1/6

ঘ.

1/9

✓ সঠিক উত্তর

ব্যাখ্যা

Total number of out comes possible when a die is rolled = 6
Hence, total number of out comes possible when a die is rolled twice, n(s) = 6

\times

$\times$ 6 = 36
E = Geting a sum of 9 when the two dice fell = {(3,6), (4,5), (5,4), (6,3)}
Hence n (E) = 4
P(E) =

\frac{n (E)}{n Unknown node type: br(S)} = \frac{4}{36} =Unknown node type: br \frac{1}{9}

$\frac{n (E)}{n (S)} = \frac{4}{36} = \frac{1}{9}$

বিষয়: গণিতটপিক: সম্ভাব্যতা (Probability)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

৪৫

Two tanks A and B are filled with petrol. Tank A holds 600 liters more than B. If 100 liters of petrol were taken out from each tank, tank A would then contain 3 times as much petrol as tank B. What is the total number of liters of fuel in the two full tanks?

ক.

1400

✓ সঠিক উত্তর

খ.

1200

গ.

1000

ঘ.

900

ব্যাখ্যা

Let, B has x litres, So A has (x + 600) litres
Accordly to the question,
(x + 500) = 3 (x - 100)

\Rightarrow

$\Rightarrow$ x + 500 = 3x – 300

\Rightarrow

$\Rightarrow$ 800 = 2x

∴

$∴$ x = 400
And total = 400 + 600 + 400 = 1400 litres.

বিষয়: গণিতটপিক: নল ও চৌবাচ্চা (Pipes and cistern)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

Two tanks A and B are filled with petrol. Tank A holds 600 liters more than B. If 100 liters of petrol were taken out from each tank, tank A would then contain 3 times as much petrol as tank B. What is the total number of liters of fuel in the two full tanks?

ক.

1400

✓ সঠিক উত্তর

খ.

1200

গ.

1000

ঘ.

900

ব্যাখ্যা

Let, B has x litres, So A has (x + 600) litres
Accordly to the question,
(x + 500) = 3 (x - 100)

\Rightarrow

$\Rightarrow$ x + 500 = 3x – 300

\Rightarrow

$\Rightarrow$ 800 = 2x

∴

$∴$ x = 400
And total = 400 + 600 + 400 = 1400 litres.

বিষয়: গণিতটপিক: নল ও চৌবাচ্চা (Pipes and cistern)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

৪৬

Six bells starts ringing logether and ring at intervals of 4, 8, 10, 12, 15 and 20 seconds respectively. How many times will they ring together in 60 minutes?

ক.

খ.

গ.

ঘ.

✓ সঠিক উত্তর

ব্যাখ্যা

LCM of 4, 8, 10, 12, 15 and 20 = 120
120 seconds = 2 minutes
Hence all the bells will ring together in every 2 minutes
Hence, number of times they will ring together in 60 minutes = 1 +

\frac{60}{2}

$\frac{60}{2}$
= 31

বিষয়: গণিতরেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

Six bells starts ringing logether and ring at intervals of 4, 8, 10, 12, 15 and 20 seconds respectively. How many times will they ring together in 60 minutes?

ক.

খ.

গ.

ঘ.

✓ সঠিক উত্তর

ব্যাখ্যা

LCM of 4, 8, 10, 12, 15 and 20 = 120
120 seconds = 2 minutes
Hence all the bells will ring together in every 2 minutes
Hence, number of times they will ring together in 60 minutes = 1 +

\frac{60}{2}

$\frac{60}{2}$
= 31

বিষয়: গণিতরেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

৪৭

Rakid lives 4km due west of Faisal's house. Asif lives 6km due north of Faisl's house and 4km due west of Hamed's house. What is the minimum distance from Rakib's house to Hamed's house?

ক.

4km

খ.

5km

গ.

8km

ঘ.

10km

✓ সঠিক উত্তর

ব্যাখ্যা

Look at the picture below:
So, distance

\sqrt{8^{2} + 6^{2}} = \sqrt{100} = 10 k m

$\sqrt{8^{2} + 6^{2}} = \sqrt{100} = 10 k m$

বিষয়: গণিতরেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

Rakid lives 4km due west of Faisal's house. Asif lives 6km due north of Faisl's house and 4km due west of Hamed's house. What is the minimum distance from Rakib's house to Hamed's house?

ক.

4km

খ.

5km

গ.

8km

ঘ.

10km

✓ সঠিক উত্তর

ব্যাখ্যা

Look at the picture below:
So, distance

\sqrt{8^{2} + 6^{2}} = \sqrt{100} = 10 k m

$\sqrt{8^{2} + 6^{2}} = \sqrt{100} = 10 k m$

বিষয়: গণিতরেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

৪৮

If a certain product that sells normally at 59 taka is on sale at two for 99 taka, then how much can Fahim save by purchasing 10 of that product?

ক.

85 taka

খ.

90 taka

গ.

95 taka

✓ সঠিক উত্তর

ঘ.

110 taka

ব্যাখ্যা

At two for 99 taka, two price of 10 product = 5

\times

$\times$ 99 = 495 tk
at original price ,, ,, ,, 10 ,, = 10

\times

$\times$ 59 = 590 tk

∴

$∴$ he saves = 590 – 495 = 95 tk.

বিষয়: গণিতরেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

If a certain product that sells normally at 59 taka is on sale at two for 99 taka, then how much can Fahim save by purchasing 10 of that product?

ক.

85 taka

খ.

90 taka

গ.

95 taka

✓ সঠিক উত্তর

ঘ.

110 taka

ব্যাখ্যা

At two for 99 taka, two price of 10 product = 5

\times

$\times$ 99 = 495 tk
at original price ,, ,, ,, 10 ,, = 10

\times

$\times$ 59 = 590 tk

∴

$∴$ he saves = 590 – 495 = 95 tk.

বিষয়: গণিতরেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

৪৯

From the profits of a certain investment, Faisal got 1/3 of the total profit and three of his friends each got 1/3 of the rest. If Faisal and one of his friends got a total of 60000 taka, what was the total profit?

ক.

90000 taka

খ.

96000 taka

গ.

108000 taka

✓ সঠিক উত্তর

ঘ.

135000 taka

ব্যাখ্যা

Let, total profit be taka x

∴

$∴$ Faisal get taka

\frac{x}{3}

$\frac{x}{3}$
So, each of the friends get

\frac{1}{3} (x - \frac{x}{3})

$\frac{1}{3} (x - \frac{x}{3})$ =

\frac{2 x}{9}

$\frac{2 x}{9}$
So

[Math Processing Error] $\frac{x}{3} +$
2x9 = 60,000

\frac{5 x}{9}

$\frac{5 x}{9}$ = 60,000

\Rightarrow

$\Rightarrow$ x =

\frac{60, 000 \timesUnknown node type: br 9}{5}

$\frac{60, 000 \times 9}{5}$

∴

$∴$ x = 1,08,000

বিষয়: গণিতটপিক: লাভ-ক্ষতি (Profit and loss)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

From the profits of a certain investment, Faisal got 1/3 of the total profit and three of his friends each got 1/3 of the rest. If Faisal and one of his friends got a total of 60000 taka, what was the total profit?

ক.

90000 taka

খ.

96000 taka

গ.

108000 taka

✓ সঠিক উত্তর

ঘ.

135000 taka

ব্যাখ্যা

Let, total profit be taka x

∴

$∴$ Faisal get taka

\frac{x}{3}

$\frac{x}{3}$
So, each of the friends get

\frac{1}{3} (x - \frac{x}{3})

$\frac{1}{3} (x - \frac{x}{3})$ =

\frac{2 x}{9}

$\frac{2 x}{9}$
So

[Math Processing Error] $\frac{x}{3} +$
2x9 = 60,000

\frac{5 x}{9}

$\frac{5 x}{9}$ = 60,000

\Rightarrow

$\Rightarrow$ x =

\frac{60, 000 \timesUnknown node type: br 9}{5}

$\frac{60, 000 \times 9}{5}$

∴

$∴$ x = 1,08,000

বিষয়: গণিতটপিক: লাভ-ক্ষতি (Profit and loss)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

৫০

A water tank with 64-gallon capacity is filled by pipe A and emptied by pipe B. If the rate of water flow through pipe A is 2 gallons per hour, how many gallons per hour should flow through pipe B so that when both pipes are open, the initially empty tank shold be full in exactly 96 hours?

ক.

3/8

খ.

4/3

✓ সঠিক উত্তর

গ.

2/3

ঘ.

8/3

ব্যাখ্যা

Let, x gallons per hour should flow through pipe B
In 1 hour A flouss 2 gallons

∴

$∴$ ,, 96 hour A ,, (96

× 2) ,, = 192 ,,
So 192 – 96x = 64

\Rightarrow x =

$\Rightarrow x =$
192 - 64 96
= 43

বিষয়: গণিতটপিক: নল ও চৌবাচ্চা (Pipes and cistern)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

A water tank with 64-gallon capacity is filled by pipe A and emptied by pipe B. If the rate of water flow through pipe A is 2 gallons per hour, how many gallons per hour should flow through pipe B so that when both pipes are open, the initially empty tank shold be full in exactly 96 hours?

ক.

3/8

খ.

4/3

✓ সঠিক উত্তর

গ.

2/3

ঘ.

8/3

ব্যাখ্যা

Let, x gallons per hour should flow through pipe B
In 1 hour A flouss 2 gallons

∴

$∴$ ,, 96 hour A ,, (96

× 2) ,, = 192 ,,
So 192 – 96x = 64

\Rightarrow x =

$\Rightarrow x =$
192 - 64 96
= 43

বিষয়: গণিতটপিক: নল ও চৌবাচ্চা (Pipes and cistern)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

৫১

If x is an integer divisible by 6 but not by 4, then which of the following CANNOT be an integer?

ক.

n/2

খ.

n/3

গ.

n/12

✓ সঠিক উত্তর

ঘ.

n/10

ব্যাখ্যা

Numbers that are divisible by 6 but not 4 are : 6, 18, 30 ..... all there numbers when divided by 12 cannot be an integer.

বিষয়: গণিতরেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

If x is an integer divisible by 6 but not by 4, then which of the following CANNOT be an integer?

ক.

n/2

খ.

n/3

গ.

n/12

✓ সঠিক উত্তর

ঘ.

n/10

ব্যাখ্যা

Numbers that are divisible by 6 but not 4 are : 6, 18, 30 ..... all there numbers when divided by 12 cannot be an integer.

বিষয়: গণিতরেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

৫২

Three friends each contributed 8000 taka to buy a computer. If they bought the computer for 19500 taka plus 10% tax, how much money will each of them get back from the inital contribution?

ক.

1950 taka

খ.

1500 taka

গ.

850 taka

✓ সঠিক উত্তর

ঘ.

650 taka

ব্যাখ্যা

8000

\times

$\times$ 3 = 24000 tk
19500 + 10% of 19500 = 21450 tk
21450 + 3 = 7150 tk
So, each of them get back Tk (8000 – 7150) = Tk 850

বিষয়: গণিতরেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

Three friends each contributed 8000 taka to buy a computer. If they bought the computer for 19500 taka plus 10% tax, how much money will each of them get back from the inital contribution?

ক.

1950 taka

খ.

1500 taka

গ.

850 taka

✓ সঠিক উত্তর

ঘ.

650 taka

ব্যাখ্যা

8000

\times

$\times$ 3 = 24000 tk
19500 + 10% of 19500 = 21450 tk
21450 + 3 = 7150 tk
So, each of them get back Tk (8000 – 7150) = Tk 850

বিষয়: গণিতরেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

৫৩

Rahat completes a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

ক.

121 km

খ.

242 km

গ.

112 km

ঘ.

224 km

✓ সঠিক উত্তর

বিষয়: গণিতটপিক: ঐকিক নিয়ম (Unitary method)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

Rahat completes a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

ক.

121 km

খ.

242 km

গ.

112 km

ঘ.

224 km

✓ সঠিক উত্তর

বিষয়: গণিতটপিক: ঐকিক নিয়ম (Unitary method)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

৫৪

In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is two-third of the number of students of 8 years of age which is 48. what is the total number of students in the school?

ক.

খ.

গ.

ঘ.

100

✓ সঠিক উত্তর

ব্যাখ্যা

Let, the number be x then
Number of students above 8 years age = (100 - 201% of x) = 80% of x

∴

$∴$ 48 +

\frac{2}{3}

$\frac{2}{3}$ of 48

\Rightarrow \frac{80}{100}

$\Rightarrow \frac{80}{100}$ x = 80

∴

$∴$ x = 100

বিষয়: গণিতটপিক: সেট (Set)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015

In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is two-third of the number of students of 8 years of age which is 48. what is the total number of students in the school?

ক.

খ.

গ.

ঘ.

100

✓ সঠিক উত্তর

ব্যাখ্যা

Let, the number be x then
Number of students above 8 years age = (100 - 201% of x) = 80% of x

∴

$∴$ 48 +

\frac{2}{3}

$\frac{2}{3}$ of 48

\Rightarrow \frac{80}{100}

$\Rightarrow \frac{80}{100}$ x = 80

∴

$∴$ x = 100

বিষয়: গণিতটপিক: সেট (Set)রেফারেন্স: Mercantile Bank Ltd - Management Trainee Officer - 31.07.2015