Modhumoti Bank Ltd || Probationary officer (21-04-2017) || 2017

1.

A, B and C started a job which they can complete in 2 days . B can do the job in 5 days and C can do it in 4 days. After working for 1 day, both B and C left. How long would it take A to complete the rest of the job?

A, B C একটি কাজ একত্রে 2 দিনে শেষ করতে পারে। B কাজটি 5 দিনে ও C কাজটি 4 দিনে শেষ করা পারে। তারা একসাথে 1 দিনে কাজ করার পর B ও C চলে গেল। বাকি কাজ A কয় দিনে করল?

A, B & C takes 2 days to complete= 1 work

A. B & C takes 1 days to complete = $\frac{1}{2}$ part of work

The rest = $(1 - \frac{1}{2})$ = $\frac{1}{2}$ part of work

Only B takes 5 days to complete 1 work

Only B takes 1 day to complete $\frac{1}{5}$ part of work

Only C takes 4 days to complete 1 work

Only C takes 1 day to complete $\frac{1}{4}$ part of work

Jointly (B+C) can do in I day= $(\frac{1}{5} + \frac{1}{4}) = \frac{9}{20}$ part of work

So, A can do in 1 day = $(\frac{1}{2} - \frac{9}{20}) = \frac{1}{20}$ part of work

A can do $\frac{1}{20}$ work in 1 day

A can do 1 work in 20 day

A can do $\frac{1}{2}$ work in $\frac{20}{2}$ = 10 days

2.

A man’s running speed is 3 times of his walking speed. He runs a distance and comes back by walking . Total time taken by him is 2 hours. What is the distance in miles if he runs 9 miles per hour?

Given, Man's running speed = 9 miles/hour

Man's walking speed = $\frac{9}{3}$ = 3 miles/hour

Given, Total time taken by the man to complete the journey is 2 hours.

Let, total distance covered by the man is x miles,

According to question,

$\frac{x}{9} + \frac{x}{3} = 2 \Rightarrow \frac{x + 3 x}{9} = 2 \Rightarrow 4 x = 18 \Rightarrow x = \frac{18}{4} = 4.5$

Distance covered by the man is 4.5 miles.

ans. The distance in miles if he runs 9 miles per hours is 4.5 miles.

3.

A shirt was sold at 6% profit . If the purchase price was 4% less and te selling price was Tk. 4 more, the profit would be 12.5% . What was the purchase price of the shirt?

At 6% profit, the selling price = 100+6= Tk. 106

& 4% less, the cost of the item = 100-4 =Tk. 96

Again, in 12.5% profit the selling price= $(96 + \frac{96 \times 12.5}{100}) = 108$ TK.

Difference between selling price = 108-106= Tk. 2

In difference of Tk. 2 the cost price = Tk. 100

In difference of Tk. 4 the cost price = Tk. $\frac{100 \times 4}{2} = 200 T K .$

4.

Solve the equation: $\frac{1}{2 x - 5} + \frac{1}{2 x - 11} = \frac{1}{2 x - 7} + \frac{1}{2 x - 9}$

$\frac{1}{2 x - 5} + \frac{1}{2 x - 11} = \frac{1}{2 x - 7} + \frac{1}{2 x - 9} \Rightarrow \frac{1}{2 x - 5} - \frac{1}{2 x - 9} = \frac{1}{2 x - 7} - \frac{1}{2 x - 11} \Rightarrow \frac{2 x - 9 - (2 x - 5)}{(2 x - 5) (2 x - 9)} = \frac{2 x - 11 - (2 x - 7)}{(2 x - 7) (2 x - 11)} \Rightarrow \frac{2 x - 9 - 2 x + 5}{4 x^{2} - 18 x - 10 x + 45} = \frac{2 x - 11 - 2 x + 7}{4 x^{2} - 22 x - 14 x + 77} \Rightarrow \frac{- 4}{4 x^{2} - 28 x + 45} = \frac{- 4}{4 x^{2} - 36 x + 77} \Rightarrow \frac{1}{4 x^{2} - 28 x + 45} = \frac{1}{4 x^{2} - 36 x + 77} \Rightarrow 4 x^{2} - 28 x + 45 = 4 x^{2} - 36 x + 77 \Rightarrow 4 x^{2} - 28 x - 4 x^{2} + 36 x = 77 - 45 \Rightarrow 8 x = 32 ∴ x = \frac{32}{8} = 4$

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