There was one mess for 30 boarders in a certain hostel. If the number of boarders is increased by 10, the expenses of the mess were increased by ` 4,000 per month, while the average expenditure per head diminished by ` 200. Find the original monthly expenses.
Answer : Option A. Average Expenditure for 40 boarders = (x + 4000)/40. The difference = x / 30 + (x + 4000)/40 = 200. Solving x = 36000
In two alloys, copper and zinc are related in the ratios of 4 : 1 and 1 : 3. 10 kg of 1st alloy, 16 kg of 2nd alloy and some of pure copper are melted together. An alloy was obtained in which the ratio of copper to zinc was 3 : 2. Find the weight of the new alloy.
Answer : Option C. In First alloy, Ratio of copper and zinc is 4:1. So the ratio will be 8:2 for 10 kg. In Second alloy, Ratio of copper and zinc is 1:3 So the ratio will be 4:12 for 16 kg. They are mixed together to get new copper and zinc ratio 12:14 Now, because of adding pure copper, resultant ratio is 3:2 and we have 12:14 which means 2x = 14. So 3x = 21. So, 9 kgs of pure copper should get added to get 3:2 ratio. So total addition of mixture is 12 + 14 + 9 = 35 kg.
An iron cube of side 10 cm is hammered into a rectangular sheet of thickness 0-5 cm. If the sides of the sheet be in the ratio 1:5, then the sides are
40 cm, 200 cm
20 cm, 100 cm
10 cm, 50 cm
None of these
Answer : Option B. 10 cm has been hammered in 0.5 cm then 10 cm / 0.5 cm = 20. So the smaller side will be 20 and the ratio of 1:5 becomes 20:100.
A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/h. The other one walks at 5.4 km/h. The train needs 8.4 and 8.5 sec respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
Answer : Option D. If the length (in km) and speed (in km) of the train is L and St resp. We have L / (St – 4.5) = 8.4/3600 and L/(St-5.4) = 8.5/3600 Thus we get two equations, 3600 L = 8.4 St – 54 and 3600 L = 8.5 St – 45.9 On Equating, we get 0.1St = 8.1St = Speed of train = 81
A train 300 m long is running at a speed of 90 km/h. How many seconds will it take to cross a 200 m long train running in the opposite direction at a speed of 60 km/h?
Answer : Option A. 90 km/h = 90 x 5/18 m/s = 25 m/s. 60 km/h = 60 x 5/18 m/s = 50/3 m/s T = D / S = (300+200) / (25 + 50/3) = 12 m/s.
A monthly fee of a student consists of a constant part and a part which varies according to the number of activity clubs he wishes to join. The fee for all activity clubs is the same. A student has to pay Rs.1,075 per month, if he enrolls in three activity clubs and Rs.950 per month, if he enrolls in two activity clubs. The total monthly bill of three students who are enrolled in four activity clubs each is
Answer : Option B. For enrolling in three activities = Rs.1075 For enrolling in two activities = Rs.950 So increase of Rs.125 for 1 more activity. Thus, for enrolling in four activities = Rs.1200 So for three students enrolling in four activities = 3 x Rs 1200 = Rs 3600
In an election, a total of 9801 votes were polled. 126 votes were invalid. The successful candidate got 5 votes for every 4 votes his opponent had. At what margin did the successful candidate win his election if there were only 2 candidates?
Answer : Option D. Total votes = 9801 But 126 votes were invalid. Effective votes are 9675 So total votes are distributed as 5x + 4x = 9675 9x = 9675 => x = 1075.
Two water taps together can fill a tank in 75/8 hours. The tap of the longer diameter takes 10 hours less than the smaller one to fill the tank separately. The time in which the smaller tap can fill the tank separately is
Answer : Option A. Two water taps together can fill a tank in 75/3 hrs. 1/(x -10) + 1/x = 8/75 => x =15/4 or 100/4 Smaller tap can fill the tank separately in 25 hours.
Meena builds a circular swimming pool of radius 5 m inside a circular garden of radius 12 m. In order to compensate the area covered due to construction of pool, she extends the radius by 'r' metres keeping the garden still circular. What is the value of V?
Answer : Option C. The area of garden is 144π And the area of swimming pool is 25π She extends the radius by r. Now the new radius of garden = 12 + r => area = π(12 + r)2 So, π(12 + r)2 – 25 π = 144π => (12 + r)2 = 169 => r = 1
How many kg of sugar costing Rs. 57.5 per kg should be mixed with 75 kg of cheaper sugar costing Rs. 45 per kg so that the mixture is worth Rs. 55 per kg?
Answer : Option B. (X x 57.5 + 75 x 45) / (X + 75) = 55 x = 300 kg.
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