A motorist and a cyclist start from A to B at the same time. A to B is 18km. The speed of motorist is 15 m/hr, more than the cyclist. After covering half the distance, the motorist rests for 30 minutes and thereafter his speed is reduced by 20%. If the motorist reaches the destination B, 15 min earlier than that of the cyclist, then find the speed of the cyclist.

Created: 3 months ago | Updated: 3 months ago

Job Solution Joint Recruitment Test Joint Recruitment Test for 3 Banks || Officer (Cash) (16-11-2018) || 2018 গণিত

101

প্রশ্নে বলা হচ্ছে, একজন মোটর আরোহী ও একজন সাইকেল আরোহী একই সময় A হতে B এর দিকে রওনা দিলেন। A হতে B এর মধ্যবর্তী দূরত্ব 18km. সাইকেল আরোহী অপেক্ষা মোটর আরোহীর গতিবেগ 15 kmph বেশি। অর্ধেক পথ যাওয়ার পর মোটর আরোহী 30 মিনিট বিশ্রাম নিলেন এবং এরপর চলার সময় তার গতিবেগ 20% কমিয়ে আনলেন। যদি মোটর আরোহী সাইকেল আরোহী অপেক্ষা 15 মিনিট পূর্বেই B তে পৌঁছান তবে সাইকেল আরোহীর গতিবেগ কত ছিল?

Here we let the speed of the cyclist is x kmph.

∴ The speed of the motorist is (x + 15) kmph.

Cyclist goes through all the path in x kmph and motorist goes half the way in (x + 15) kmph and other half the way in 80% of (x + 15) kmph, that's why we can write down.

$\frac{18}{x} - [\frac{9}{x + 15} + \frac{9}{80 % o f (x + 15)}] = \frac{15 + 30}{60} \Rightarrow \frac{18}{x} - [\frac{9}{x + 15} + \frac{9}{\frac{4 (x + 15)}{5}}] = \frac{45}{60} \Rightarrow \frac{18}{x} [\frac{9}{x + 15} + \frac{45}{4 (x + 15)}] = \frac{45}{60} \Rightarrow \frac{18}{x} - \frac{9}{x + 15} - \frac{45}{4 (x + 15)} = \frac{3}{4} \Rightarrow \frac{x}{2} - \frac{1}{x + 5} - \frac{5}{4 (x + 15)} = \frac{1}{12} [D i v i d i n g b y 9] \Rightarrow \frac{2 \times 4 (x + 15) - 4 x - 5 x}{4 (x + 15)} = \frac{1}{12} \Rightarrow (8 x + 120 - 9 x) \times 12 = 4 x^{2} + 60 x \Rightarrow (120 - x) \times 12 = 4 x^{2} + 60 x \Rightarrow 1, 440 - 12 x = 4 x^{2} + 60 x \Rightarrow 4 x^{2} + 60 x + 12 x - 1400 = 0 \Rightarrow 4 x^{2} + 72 x - 1400 = 0 \Rightarrow x^{2} + 30 x - 12 - 360 = 0 \Rightarrow x (x + 30) - 12 (x + 30) = 0 \Rightarrow (x + 30) (x - 12) = 0 A s, s p e e d c a n' t b e n e g a t i v e, s o x = - 30 i s n o t a c c e p t a b l e . ∴ x = 12 ∴ T h e s p e e d o f t h e m o t o r c y c l i s t i s 12 k m p h .$

3 months ago

0 0

স্বপ্নদর্শী

Verified

A man has donated 30% of his property as charity and then gave the rest to his wife. The wife has contributed 50% of her property as charity. If wife has contributed Tk. 21,000 what was the contribution of the man as charity?

Created: 3 months ago | Updated: 3 months ago

Job Solution Joint Recruitment Test Joint Recruitment Test for 4 Banks || Trainee Senior Officer (IT/ICT) (15-12-2018) || 2018 গণিত

199

Add Description

In a restaurant, the cost of an identical three-item lunch for five people was Tk. 900. The main item cost thrice as much as the desert and the desert cost twice as much as the starter. How much did the main item cost for each person?

Created: 3 months ago | Updated: 3 months ago

Job Solution Joint Recruitment Test Joint Recruitment Test for 4 Banks || Trainee Senior Officer (IT/ICT) (15-12-2018) || 2018 গণিত

197

Add Description

A rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn, which has an area of $240 m^{2}$ . If the width of . the path is 3m and the length of the plot is greater than its breadth by 2m, what is the area of the rectangular plot?

Created: 3 months ago | Updated: 3 months ago

Job Solution Joint Recruitment Test Joint Recruitment Test for 6 Banks || Senior Officer (02-08-2019) || 2019 গণিত

209

Add Description

A pipe can fill a tank in 0.9 hours and another pipe can empty in 0.7 hours. If tank is completely filled and both pipes are opened simultaneously then 450 liters of water is removed from the tank in 2.5 hours. What is the capacity of the tank?

Created: 3 months ago | Updated: 3 months ago

Job Solution Joint Recruitment Test Joint Recruitment Test for 6 Banks || Senior Officer (02-08-2019) || 2019 গণিত

203

Add Description

A sum of Tk. 3,240 was fixed to complete a work. 54 workers completed the work in 8 days and the sum was divided equally among the workers. If the work was to be completed in 3 days then how much less money each worker would receive compared to when the work work was completed in 8 days?

Created: 3 months ago | Updated: 3 months ago

Job Solution Joint Recruitment Test Joint Recruitment Test for 6 Banks || Senior Officer (02-08-2019) || 2019 গণিত

188

Add Description

Related Questions

A man has donated 30% of his property as charity and then gave the rest to his wife. The wife has contributed 50% of her property as charity. If wife has contributed Tk. 21,000 what was the contribution of the man as charity?

In a restaurant, the cost of an identical three-item lunch for five people was Tk. 900. The main item cost thrice as much as the desert and the desert cost twice as much as the starter. How much did the main item cost for each person?

A pipe can fill a tank in 0.9 hours and another pipe can empty in 0.7 hours. If tank is completely filled and both pipes are opened simultaneously then 450 liters of water is removed from the tank in 2.5 hours. What is the capacity of the tank?

A sum of Tk. 3,240 was fixed to complete a work. 54 workers completed the work in 8 days and the sum was divided equally among the workers. If the work was to be completed in 3 days then how much less money each worker would receive compared to when the work work was completed in 8 days?