A string is 148 cm long. It is cut into 3 pieces. The longest piece is 4 times as long as the middle-sized
piece & the shortest piece is 77 cm shorter than the longest piece. Find the length of the shortest piece (in cm).
A is 20 years older than B who is five times as old as C. The total of the ages of A, B and C is 174 years. What is the value when the square of age of B is multiplied to the sum of ages of A and C ?
Two persons are on either sides of a tower of height 150 m. The persons observers the top of the tower at an angle of elevation of 45Â° and 60Â°. If a car crosses the distance between these two persons in 15 seconds, what is the speed of the car?
OPtion
1) 15.77 km/hr
2) 31.144 km /hr
3) 34.02 km /hr
4) 54.10 km /hr
5) 56.784 m/s
6) 16.784 km /hr
7) 56.10 km /hr
8) 56.784 km /hr
9) 16.63 km /hr
10) None of these
Solution
Let BD be the tower and A and C be the positions of the persons.
Given that BD = 150 m, angle BAD = 45Â°, angle BCD = 60Â°
From the right ABD,
tan 45Â° = BD/BA
=> BD = BA = 150 m
From the right CBD,
tan 60Â° = BD/BC
=> BC = 150/âˆš3
Distance between the two persons = AC = BA + BC
AC = 150 + 150/âˆš3 = 150 + 86.60 = ~236.60 m
Speed of car = Distance / time = 236.60/15 = 15.77 m/sec = 56.784 km/hr
Mr. Ramanujam asked his students to find the sum of all pages of their maths book. Chatur gave the answer as 8554.The teacher told him that he has not added one page.
Find the page number which the Chatur forgot to add?
A mixture contains sugar solution and colored water in the ratio 2 : 3. If 24 liters of colored water is added to the mixture, the ratio becomes 2 : 5. Find the initial quantity of sugar solution in the given mixture (in liters).
The initial ratio is 2 : 3
Let â€˜kâ€™ be the common ratio.
=> Initial quantity of sugar solution = 2 k
=> Initial quantity of colored water = 3 k
=> Final quantity of sugar solution = 2 k
=> Final quantity of colored water = 3 k + 24
Final ratio = 2 k : 3 k + 24 = 2 : 5
=> k = 12
Therefore, initial quantity of sugar solution in the given mixture (in liters) = 2 *12 = 24 liter
Total percentage of students from Maharashtra = 35%
Percentage of Mumbai students among 35% of Maharashtra students = 20%
Total percentage of students from Mumbai = 20% of 35 = (35*20)/100 = 7%