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, 14x8y=57
=7x4y=57 =xy=2049 ∴x : y = 20 : 49 Again, 8y7z=78 =yz=4964 ∴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 13 full, a leak develops in the tank through which 13 water supplied by both the pipes goes out. How much time will the tank take to be full?
In 1 hour, A and B together can fill = 120+130=3+260=560=112 part of the tank ∴Before laekage, both pipe would take to fill 13 part of the tank =13112=13×121=4 hours Now, in 1 hour, both pipes can fill up the tank effectively = 112×23=118part Remainting (1-13) =23 part of the tank will take = 23118=23×181=12 hours ∴Total time required = 4+12=16 hours (ans.)
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?
Let, principal amount of x; and rate of compound interest be r; time, n= ? apply the law of compound interest , we can write x(1+r100)3=8x =(1+r100)3=8xx=8 ∴(1+r100)3=8....................(i) Now, according to question, x (1+r100)n=16x =(1+r100)n=16 =(1+r100)n=24 =(1+r100)=2(3×43) =(1+r100)n=843 ={(1+r100)3}n33}43 =n3 =43 ∴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.
After 100 days, remaining work = (1-2.515)=(1-16)=6-16=56 part of work Remaining days = 300-100=200 days Now, 16 part of work is done in 100 days by 45 men ∴56 part of work is done in 200 days by =45×100×6×5200×6=112.5=113 men ∴Number of extra men needed = 113-45 = 68 (ans.)
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?
The bucket contained x liters of A and y liters of B Given that, xy=73 ∴x=7y5...........(i) and y = 5x7........(ii) sum of ratio = 5+7=12 Now, in 9 liters of replaced mixture, the amount of A was = 712×9=214 part and the amount of B was = 9-214=36-214=154 part According to question, x-214y-154+9=79 =x-2145x7+214=79 =9x-1894=5x+1474 =4x=1894+1474 =189+1474 =3364=84 ∴x=844=21