From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 60° and 45° respectively. If the bridge is at a height of 9 meter from the banks then find the width of the river? Assume both the banks are at same ground level.
OPtion
1) 14.02 m
2) 14.11 m
3) 14.20 m
4) 14.40 m
5) 14.73 m
6) 14.35 m
7) 14.05 m
8) 14.53 m
9) 14.63 m
10) None of these
Solution
Let A and B be the two sides of the river and C be the point on the bridge. D is a point on straight line between A and B such that CD = 9 meters
Width of the river would = AD+BD
In right angled triangle ACD,
tan 60° = CD/AD
=> √3 = 9/AD
=> AD = 9/√3 = 3√3
In right angled triangle BCD,
tan 45° = CD/BD
=> 1 = CD/BD
=> CD = BD = 9 meters
So the width of the river is AD+BD = 9+3√3 = ~14.20 meters
A certain number of men can finish a piece of work in 30 days. If however there were 15 men less it will take 30 days more for the work to be finished. How many men were there originally?
A certain number of men can finish a piece of work in 30 days. If however there were 15 men less it will take 30 days more for the work to be finished.
So the no. of days are doubled (from 30 to 60) , it means no. is men is reduced to half.
so earlier, there were 15*2= 30 men.
Initially two cups of same volume are present with milk filled upto 2/7th and 3/7th of their volumes. Water is then filled in both the cups (completely). Then two mixtures are mixed. Find the ratio of water to milk in the mixture?
Let the cups volume be x.
here we assume that water fills both volumes completely
after mixing , total milk is -> 2/7x + 3/7x = 5/7x
after mixing , total water is -> 5/7x + 4/7x = 9/7x
therefore water to milk ratio is (9/7)/(5/7) = 9:5
A programmer has the capability of thinking 70 lines of code in six minutes and can type 70 lines of code in 12 minutes. He takes a break for six minutes after every 12 minutes. How many lines of codes will he complete writing in 72 minutes?
Assume that he always needs to think before writing any code?
So five times for 6 minutes he types/writes code, total minutes he spends typing the code = 6*5 = 30 minutes
In 12 Minutes he can type 70 lines of code
In 30 minutes he types (70/12)*30 = 175 lines
A tempo, while travelling at 75 kmph, uses 25% more petrol than it uses while travelling at 50 kmph for travelling a certain distance. Using one liter of petrol, it can travel 22.5 km at 50 kmph. How far can the tempo travel on 15 liters of petrol at a speed of 75 kmph?
An Office used three types of envelopes: small,medium and large. They used 160 small envelopes. The no.of Medium envelopes used was 5 times the no. of small envelopes plus 5/20 of the total number of envelopes. The no. of large envelopes was equal to the no. of small envelopes plus 5/20 of the no. of medium envelope. Altogether, How many envelope did they use?
At the time of marriage, a man was 5 years elder to his wife. 16 years after their marriage, his age is 8/7 times the age of his wife. What was wife's age at the time of marriage ?
A person spends 20% of his salary on food, 35% on house rent, 20% on conveyance and 10% of the remaining on entertainment. If his savings at the end of the month is Rs. 23700, then his salary per month in rupees is: