7 pices
Let, Brand X pen = p pieces
Brand Y pen = (12 —p) pieces
Cost of p pieces = 4 x p = 4p Tk.
Cost of (12 —p) pieces = Tk. (12 —p) x 2.8
According to the question,
4p + (12-p) 2.8 = 42
=> 4p + 33.6 — 2.8p = 42
=> 4p — 2.8p = 42 — 3306
=> 1.2p = 8.4
=> p = 7
70
Ratio of Mr. Zaman & Mr. Younus = 4 : 3
Sum oftheratio=4+3=7
Total number of voters = 581
Voters who apply their votes = 581 – 91 = 490
Mr. Zaman got = 490 x $\frac{4}{7}$= 280
Mr. Yunus got = 490 x $\frac{3}{7}$= 210
The margin of votes = 280 — 210 = 70
TK 10500
Let the pay of one officer Tk. x
The pay of second officer = Tk.(24,000 – x)
At 9% decrease, the pay of one officer become = x — 9% of x
= $\frac{91x}{100}$
At 17% increase, the pay of second officer become = Tk. $\frac{117(24000-x)}{100}$
According to question
$\frac{91x}{100}$ = $\frac{117(24000-x)}{100}$
=> 91x = 2808000 — 117x
=> 91x + 117x= 2808000
=> 208x = 2808000
x = 13500
Pay of one officer = Tk. 13500
Pay of second officer = Tk. (24000 – 13500) = Tk. 10500.
60 students
Suppose, the number of students were at
Per head amounts = $\frac{3000}{x}$ Tk.
As 10 students did not turn up then charged amount Will be $\frac{3000}{x-10}$ Tk.
Per head amounts = Tk.$\frac{3000}{x-10}$10
According to the question
$\frac{3000}{x-10}$ – $\frac{3000}{x}$ =10
=> $\frac{3000x-3000x+30000}{(x-10)x}$ =10
=> x²—10x—3000=0
=> x² — 60x+ 50x— 3000 = 0
=> x (x—60) + 50 (x— 60) = 0
=> (x+ 50) (x—60) = 0
=> x — 60 = 0 [Negative value ignored]
=> x= 60
30 days required for the two of them together to complete the whole work.
In 80 days. Abir can do 1 portion of work
In 10 days. Abir can do $\frac{1 x 10}{80}$ portion of work
The rest of the work = 1 —$\frac{1 }{8}$ = $\frac{7}{8}$ portion.
Now Bashir takes 42 days to complete = $\frac{7}{8}$ portion of the work
Now Bashir takes 1 days to complete = $\frac{7}{8×42}$ portion of the work
= $\frac{1}{48}$ portion of the work
In 1 day Abir & Bashir together can do = $\frac{1}{80}+\frac{1}{48}$ portion
= $\frac{1}{30}$ portion
$\frac{1}{30}$ portion of the work they can do in = 1 day
1 portion of the work they can do in = 1 x 30 = 30 day
600 ft and 400 ft
Suppose the office is like these:
Let the wide of the first portion is x feet, then the wide of the second portion become (1000 —x) feet,
According to question,
2 (x +1000)— 2 (1000 —x +1000)= 400
=> 2x + 2000 — 4000 + 2x = 400
=> 4x = 400 + 2000
=> x = 600
So, width = 1000 — 600 = 400 feet.
