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Joint Recruitment for 8 Banks || Senior Officer (05-06-2019) || 2019

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Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

Let, their investments are = x, y & z

$∴$ The first partner's investment will be 14x Tk.

Second partner's investment will be 8y Tk.

Third partner's investment will be 7z Tk.

So we get from above information, $\frac{14 x}{8 y} = \frac{5}{7}$

$= \frac{7 x}{4 y} = \frac{5}{7} = \frac{x}{y} = \frac{20}{49} ∴ x : y = 20 : 49 A g a i n, \frac{8 y}{7 z} = \frac{7}{8} = \frac{y}{z} = \frac{49}{64} ∴ y : z = 49 : 64 ∴ x : y : x = 20 : 49 : 64$

Two pipes A and B can fill a tank in 20 hours and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is $\frac{1}{3}$ full, a leak develops in the tank through which $\frac{1}{3}$ water supplied by both the pipes goes out. How much time will the tank take to be full?

$I n 1 h o u r, A a n d B t o g e t h e r c a n f i l l = \frac{1}{20} + \frac{1}{30} = \frac{3 + 2}{60} = \frac{5}{60} = \frac{1}{12} p a r t o f t h e t a n k ∴ B e f o r e l a e k a g e, b o t h p i p e w o u l d t a k e t o f i l l \frac{1}{3} p a r t o f t h e \tan k = \frac{\frac{1}{3}}{\frac{1}{12}} = \frac{1}{3} \times \frac{12}{1} = 4 h o u r s N o w, i n 1 h o u r, b o t h p i p e s c a n f i l l u p t h e \tan k e f f e c t i v e l y = \frac{1}{12} \times \frac{2}{3} = \frac{1}{18} p a r t R e m a i n t i n g (1 - \frac{1}{3}) = \frac{2}{3} p a r t o f t h e \tan k w i l l t a k e = \frac{\frac{2}{3}}{\frac{1}{18}} = \frac{2}{3} \times \frac{18}{1} = 12 h o u r s ∴ T o t a l t i m e r e q u i r e d = 4 + 12 = 16 h o u r s (a n s .)$

A finance company declares that, at a certain compound interest rate, a sum of money deposited by anyone will become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will it become 16 times?

$L e t, p r i n c i p a l a m o u n t o f x; a n d r a t e o f c o m p o u n d i n t e r e s t b e r; t i m e, n = ? a p p l y t h e l a w o f c o m p o u n d i n t e r e s t, w e c a n w r i t e x {(1 + \frac{r}{100})}^{3} = 8 x = {(1 + \frac{r}{100})}^{3} = \frac{8 x}{x} = 8 ∴ {(1 + \frac{r}{100})}^{3} = 8 . . . . . . . . . . . . . . . . . . . . (i) N o w, a c c o r d i n g t o q u e s t i o n, x {(1 + \frac{r}{100})}^{n} = 16 x = {(1 + \frac{r}{100})}^{n} = 16 = {(1 + \frac{r}{100})}^{n} = 2^{4} = (1 + \frac{r}{100}) = 2^{(3 \times \frac{4}{3})} = {(1 + \frac{r}{100})}^{n} = 8^{\frac{4}{3}} = {{(1 + \frac{r}{100})}^{3}}^{\frac{n}{3}}^{3}}^{\frac{4}{3}} = \frac{n}{3} = \frac{4}{3} ∴ n = 4$

An engineer undertake a project to build a road 15km long in 300 days and employs 45 men for the purpose. After 100 days, he finds 2.5km of the road has been completed. Find the number of extra men he must employ to finish the work in time.

$A f t e r 100 d a y s, r e m a i n i n g w o r k = (1 - \frac{2.5}{15}) = (1 - \frac{1}{6}) = \frac{6 - 1}{6} = \frac{5}{6} p a r t o f w o r k R e m a i n i n g d a y s = 300 - 100 = 200 d a y s N o w, \frac{1}{6} p a r t o f w o r k i s d o n e i n 100 d a y s b y 45 m e n ∴ \frac{5}{6} p a r t o f w o r k i s d o n e i n 200 d a y s b y = \frac{45 \times 100 \times 6 \times 5}{200 \times 6} = 112.5 = 113 m e n ∴ N u m b e r o f e x t r a m e n n e e d e d = 113 - 45 = 68 (a n s .)$

A bucket contains a mixture of two liquids A and B in the proportion 7 : 5. If 9 liters of mixture is replaced by 9 liters of liquid B, then the ratio of the two liquids becomes 7 : 9. How much of the liquid A was there in the bucket?

$T h e b u c k e t c o n t a i n e d x l i t e r s o f A a n d y l i t e r s o f B G i v e n t h a t, \frac{x}{y} = \frac{7}{3} ∴ x = \frac{7 y}{5} . . . . . . . . . . . (i) a n d y = \frac{5 x}{7} . . . . . . . . (i i) s u m o f r a t i o = 5 + 7 = 12 N o w, i n 9 l i t e r s o f r e p l a c e d m i x t u r e, t h e a m o u n t o f A w a s = \frac{7}{12} \times 9 = \frac{21}{4} p a r t a n d t h e a m o u n t o f B w a s = 9 - \frac{21}{4} = \frac{36 - 21}{4} = \frac{15}{4} p a r t A c c o r d i n g t o q u e s t i o n, \frac{x - \frac{21}{4}}{y - \frac{15}{4} + 9} = \frac{7}{9} = \frac{x - \frac{21}{4}}{\frac{5 x}{7} + \frac{21}{4}} = \frac{7}{9} = 9 x - \frac{189}{4} = 5 x + \frac{147}{4} = 4 x = \frac{189}{4} + \frac{147}{4} = \frac{189 + 147}{4} = \frac{336}{4} = 84 ∴ x = \frac{84}{4} = 21$

Job Solution | Joint Recruitment Test

Joint Recruitment for 8 Banks || Senior Officer (05-06-2019) || 2019

All

গণিত

Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

A finance company declares that, at a certain compound interest rate, a sum of money deposited by anyone will become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will it become 16 times?

An engineer undertake a project to build a road 15km long in 300 days and employs 45 men for the purpose. After 100 days, he finds 2.5km of the road has been completed. Find the number of extra men he must employ to finish the work in time.

A bucket contains a mixture of two liquids A and B in the proportion 7 : 5. If 9 liters of mixture is replaced by 9 liters of liquid B, then the ratio of the two liquids becomes 7 : 9. How much of the liquid A was there in the bucket?

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