A mixture contains sugar solution and colored water in the ratio 3 : 5. If 16 liters of colored water is added to the mixture, the ratio becomes 4 : 7. Find the initial quantity of colored water in the given mixture (in liters).
The initial ratio is 3 : 5
Let â€˜kâ€™ be the common ratio.
=> Initial quantity of sugar solution = 3 k
=> Initial quantity of colored water = 5 k
=> Final quantity of sugar solution = 3 k
=> Final quantity of colored water = 5 k + 16
Final ratio = 3 k : 5 k + 16 = 4 : 7
=> 21 k = 20k + 64
=> k = 64
Therefore, initial quantity of colored water in the given mixture (in liters) = 5 * 64 = 320 liter
When A covers 500m B Covers 470m
When A Covers 500m C covers 480
A : B = 500 : 470
A : C = 500 : 480
C/B = (C/A*A/B) = (480/470) = 480:470
When C covers 480 m, B covers 470 m.
When C covers 1200 m, B covers (470/480)*1200)m = 1175m
Therefore, C beats B by (1200 - 1175) m = 25 m.
A letter is randomly picked from the following longest word in the dictionary: pneumonoultramicroscopicsilicovolcanoconiosis
what is the probability that it is a vowel?
Sweety went to buy eleven chocolates worth Rs. x. She gave Rs.100 rupee note to the shopkeeper to buy the chocolates then shopkeeper gave rest of the money in the denominations of 50 paise, 2 rupee, and 5 rupees. If the ratio of the number of coins is 7:6:7 respectively. Then what is the price of eight chocolates?
Venkateshwara could either walk or drive to office. The time taken to walk to the office is 11 times the driving time. One day, his wife took the car making him walk to office. After walking 1.5 km, he reached a temple when his wife called to say that he can now take the car. Venkateshwara figured that continuing to walk to the office will take as long as walking back home and then driving to the office. Calculate the distance between the temple and the office in KMs.
Suppose the distance between his home and office is x km. Then, distance between his office and temple is (x â€“ 1.5) km.
If he walks at a speed of y km/hr. Then his driving speed = 11y km/hour, as he is 11 times faster in car.
Then,
Time Taken To walk back Home from temple + Time Taken to drive to office from home = Time taken to walk to office from temple
3/2y + x/11y = (x â€“ 3/2)/y
Or, 3 = 10x/11
Or, x = 33/10
Finally, x â€“ 1.5 = 33/10 - 3/2 = (33-15)/10 = 18/10 = 9/5
Option 3)
Mean x = Sum of nos. / Count of numbers = 585/9 = 65 = x
Median y = Middle term when number are arranged in ascending order = 63 = y
Mode z = Number which is present maximum number of times = 81 = z
=> x*y*2*z/5 = 65*63*2*81/5 = 132678
Pure mathematics is the world's best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It's free. It can be played anywhere - Archimedes did it in a bathtub.
Richard J. Trudeau, Dots and Lines
Small minds discuss persons. Average minds discuss events. Great minds discuss ideas. Really great minds discuss mathematics.