Ratio - Study Mode
[#76] The Lucknow-Indore Express without its rake can go 24 km an hour, and the speed is diminished by a quantity that varies as the square root of the number of wagon attached. If it is known that with four wagons its speed is 20 km/h, the greatest number of wagons with which the engine can just move is
Correct Answer
(C) 143
Explanation
Solution: Speed = $$24 - { ext{k}}sqrt { ext{n}} $$ Putting the value, n = 4 we get, k = 2 Now the equation (as k = 2) become,
S = $$24 - { ext{k}}sqrt { ext{n}} $$ Thus, it means when n = 144, speed will be zero. Hence, train can just move when 143 wagons are attached
[#77] If x varies as y then x 2 + y 2 varies as
Correct Answer
x + y
Explanation
Solution: Given, x = y Or, x - y = 0 Or, (x - y) 2 = 0 Or, x 2 + y 2 - 2xy = 0 Or, x 2 + y 2 = 2xy It means that, x 2 + y 2 varies as xy
[#78] Brindavan Express leave Chennai Central Station every day at 07.50 am and goes to Bangalore City Railway station. This train is very popular among the travelers. On 25th July 2012 number of passengers traveling by I class and II class was in the ratio 1 : 4. The fare for this travel is in the ratio 3 : 1. The total fare collected was Rs. 224000. (Rs. Two lakhs twenty four thousand only). What was the fare collected from I class passengers on that day?
Correct Answer
(B) Rs. 96,000
Explanation
Solution: Let the number of passenger traveling by first class be x Then, number of passenger traveling by second class will be 4x But the fare is in the ratio 3 : 1 In other words, if 3y fare is collected per I class passenger, y would be collected per II class passenger Fares of I class passengers : Fares of II class passengers = x × 3y : 4x × y = 3 : 4 The above ratio can be interpreted as follows
If total fare is 3 + 4 = 7, then I class passengers should pay Rs. 3 Similarly, we can calculate the fare of I class passengers when total was 224000 Total Fare Class Fare 7 3 224000 ? = $$224000 imes frac{3}{7}$$ = Rs. 96000
[#79] A vessel of capacity 2 litre has 25% alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. what is the new concentration of mixture ?
Correct Answer
(A) 29%
Explanation
Solution: Amount of alcohol in first vessel,
= 25% of 2 litre = 0.25 × 2 = 0.5 litre Amount of alcohol in second vessel, = 40% of 6 litre = 0.4 × 6 = 2.4 litre Total amount of alcohol out of 10 litres of mixture is 0.5 + 2.4 = 2.9 litre Thus, Concentration of the mixture is, $$frac{{2.9 imes 100}}{{10}}$$ = 29%
[#80] The number of oranges in three basket are in the ratio 3 : 4 : 5. In which ratio the no. of oranges in first two basket must be increased so that the new ratio becomes 5 : 4 : 3 ?
Correct Answer
(D) 2 : 1
Explanation
Solution: Let, B 1 : B 2 : B 3 = 3x : 4x : 5x and B 1 : B 2 : B 3 = 5y : 4y : 3y Number of oranges remain constant in third basket as increase in oranges takes place only in first two baskets. Hence,
5x = 3y
x = $$frac{3y}{5}$$
and,
∴ 3x : 4x : 5x (putting the vale of x) = $$frac{{9{ ext{y}}}}{5}:frac{{{ ext{12y}}}}{5}:frac{{{ ext{15y}}}}{5}$$ = 9y : 12y : 15y And, 5y : 4y : 3y (multiple by 5) → 25y : 20y : 15y ∴Increment in first basket = 16
And, Increment in second basket = 8
Thus, Required ratio = $$frac{{16}}{8}$$ = 2 : 1