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Sonali Bank Ltd. || Officer (Cash) (2019) || 2019

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A man covers a certain distance on a toy train. Had the train moved 4 km/hr faster, it would have taken 30 minutes less. If it moved 2 km/hr slower, it would taken 20 minutes more. Find the distance.

প্রশ্নে বলা হচ্ছে, একজন লোক টয় ট্রেনে একটি নির্দষ্ট দূরত্ব অতিক্রম করে। যদি ট্রেনটি 4 মিনিট/ঘণ্টা বেশি গতিতে ছুটত তবে 30 মিনিট কম লাগত। যদি 2 কিমি/ঘণ্টা কম গতিতে চলত তবে 20 মিনিট বেশি লাগে । দূরত্ব বের করুন।

The distance be x km and initial speed by y km/hr.

Original time taken $\frac{D i s \tan c e}{S p e e d} = \frac{x}{y}$

According to the first condition , $\frac{x}{y} - \frac{x}{y + 4} = \frac{30}{60} ∵ [30 m i n u t e s = \frac{30}{60} h o u r s]$

$\Rightarrow \frac{x y + 4 x - x y}{y (y + 4)} = \frac{1}{2}$

$\Rightarrow \frac{4 x}{y (y + 4)} = \frac{1}{2}$

$\Rightarrow 8 x = y^{2} + 4 y$

$∴ = \frac{y^{2} + 4 y}{8} . . . . . . . . . . . (i)$

Again, $\frac{x}{y - 2} - \frac{x}{y} = \frac{20}{60}$

$\Rightarrow \frac{x y - x y + 2 x}{y (y - 2)} = \frac{1}{3}$

$\Rightarrow 6 x = y^{2} - 2 y$

$∴ x = \frac{y^{2 - 2 y}}{6} . . . . . . . . . . . . . (i i)$

From equation (i) & (ii) we get have

$\frac{y^{2} + 4 y}{8} = \frac{y^{2} - 2 y}{6}$

$\Rightarrow 6 y^{2} + 24 y = 8 y^{2} - 16 y$

$\Rightarrow 8 y^{2} - 6 y^{2} = 24 y + 16 y \Rightarrow 2 y^{2} = 40 y$

∴ $y = \frac{40}{2} = 20$

Putting the value of y = 20 in equation (i)

$x = \frac{y^{2} + 4 y}{8} = \frac{{(20)}^{2} + (4 \times 20)}{8} = \frac{480}{8} = 60 k m (a n s w e r)$

Machine A, working alone at its constant rate, produces x pounds of peanut butter in 12 minutes. Machine B, working alone at its constant rate, produces x pounds of peanut butter in 18 minutes. How many minutes will it take machines A and B, working simultaneously at their respective constant rates, to produce x pounds of peanut butter?

প্রশ্নে বলা হচ্ছে যে, A মেশিন তার নির্দিষ্ট হারে চলে 12 মিনিটে x পাউন্ড Peanut butter তৈরী করে এবং B মেশিন তার নির্দিষ্ট হারে চলে 18 মিনিটে x পাউন্ড Peanut butter তৈরী করে। এখন প্রশ্ন হলো A এবং B একত্রে কাজ করে x পাউন্ড Peanut butter তৈরী করতে কত সময় নিবে?

A can produce in 12 minutes x pound of peanut butter

∴ A can produce in 1 minute $\frac{x}{12}$ pound of peanut butter

Again, B can produce in 18 minutes x pound of peanut butter

So, in 1 minute (A + B) can produce $= (\frac{x}{12} + \frac{x}{18}) = \frac{5 x}{36} P o u n d s$

Now, $\frac{5 x}{36}$ pounds can be produced by (A + B) in = 1 minute

∴ x pounds can be produced by (A + B) in $= \frac{36 \times x}{5 x}$ = 7.2 minutes = 7 minutes 12 seconds. (ans.)

Tow trains running at the rate of 75km and 60km an hour respectively on parallel rails in opposites directions, are to pass each other in 8 seconds and when they are running in the same direction at the same rates as before, a person sitting in the faster train observes that he passes the other in 33 $\frac{1}{2}$ seconds. Find the lengths of the trains.

Job Solution | Sonali Bank Ltd

Sonali Bank Ltd. || Officer (Cash) (2019) || 2019

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