বাংলাদেশ ব্যাংক এডি ২০০৬: গণিত (ব্যাখ্যাসহ সমাধান)

01 Mar 2017

1. Mr. Zaman won an election where the ratio of his votes and those of his opponent, Mr. Yunus, was 4:3.The total number of voters was 581, of which 91 did not vote. Calculate the margin of votes by which Mr. Yunus was defeated?

Solution:
Total number of voters = 581

Casted votes = 581 – 91 = 490

Mr. Zaman got = 490 ✕ (4/7) = 280

Mr. Yunus got = 490 ✕ (3/7) = 210

The margin of defeat = 280 – 210 = 70 Ans.

2. The sum of the pay of two officers is Taka 24,000 per month. If the pay of one officer is decreased by 9% and the pay of the second is increased by 17%, their pays become equal. Find the pay of each officer.

Solution:

Let, the payment of first officer = x tk

Payment of second officer = (24000 – x) tk

At 9% decrease, payment of first officer become = x – 9x/100 = 91x/100

tk

At 17% increase, payment of second officer become = (24000 – x) ✛

17% of (24000–x)

= (24000 – x)(1 ✛ 17/100) = 117(24000 – x)/100

According to the Question,

91x/100 = 117(24000 – x)/100

Or, 91x = 117(24000 – x)

Or, 91x = 117 ✕ 24000 – 117x

Or, 91x ✛ 117x = 117 ✕ 24000

Or, 208x = 117 ✕ 24000

Or, x = (117 ✕ 24000)/208

Or, x = 13,500

Payment of first officer = 13500 Tk

Payment of second officer = 24000 – 13500 = 10500 Tk Ans.

3. A Group of students has hired a bus for Taka 3000 for going to a picnic. They had an understanding that each participant would share the charge in equal amounts. But because of 10 students not turning up, the charged per student increased by Taka 10 over the initial estimates. What was the number of students who originally registered for the picnic?

Solution:

Let, total number of students = x

Per head proposed cost for the picnic = 3000/x Tk

Due to absence of 10 students, average cost charged = 3000/(x – 10) Tk

According to the Question,

3000/x – 3000/(x – 10) = 10

Or, (3000x – 3000x ✛ 30000)/x(x-10) = 10

Or, 10×2 – 10x = 30000

Or, x2 – 10x – 3000 = 0

Or, x2 – 60x ✛ 50x – 3000 = 0

Or, (x – 60)(x ✛ 50) = 0

So, x = 60 (number of students cannot be negative) Ans.

4. A square office, 1000 feet by 1000 feet, is to be partitioned into two offices by a single interior wall. The difference between the perimeters of the resulting two officers is 400 feet. What are their dimensions?

Solution:

Let, width of first portion after partition = x

So, width of second portion other side = 1000 – x

According to the Question,

2(1000 ✛ x) – 2(1000 ✛ 1000 – x) = 400

Or, 2000 ✛ 2x – 4000 ✛ 2x = 400

Or, 4x = 2000 ✛ 400

Or, x = 600

So, width of first portion = 600 ft

Width of other side = 1000 – 600 = 400 ft

So, dimensions of 1st office = 1000 ✕ 600 = 600000 sq. ft.

And, dimensions of 2nd office = 1000 ✕ 400 = 400000 sq. ft. Ans.

5. Abir can do a piece of work in 80 days. He works for 10 days and then Bashir alone finishes the rest of the work in 42 days. How much time would it take for the two of them together to complete the whole work?

Solution:

In 80 days, Abir can do 1 (whole) portion of work

In 1 day, Abir can do (1/80) part of the work

In 10 days Abir can do (1  ✕  10)/80 = 1/8 part of the work

Rest of the work = 1 – (1/8) = 7/8 part of the work

Now, in 42 days, Bashir can do 7/8 part of the work

In 1 day, Bashir can do (7/8)  ✕  42 = 1/48 part of the work

In 1 day, Abir and Bashir together can do = (1/80 ✛ 1/48) = (3 ✛ 5)/240 = 1/ 30 part of the work

So, they can do 1/30 works in 1 day

Or, they can do 1 works in 30/1= 30 days Ans.