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Sapient Technical Questions
Posted on :21-03-2016
Q1. 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.
A) 36,000B) 41,000C) 39,000D) 48,000
Explanation:30 boarders = xAverage expenditure for 30 boarders= x / 3040 boarders = x + 4000Average Expenditure for 40 boarders=x / 40 + 4000The difference = x / 30 + x / 40 – 4000 = 200x = 36000
Q2. 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.
A) 45 kgB) 40 kgC) 35 kgD) 50 kg
Explanation: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 1:3So the ratio will be 4:12 for 16 kg.They are mixed together to get new copper and zinc ratio 12:14Now, 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.
Q3. 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
A) 40 cm, 200 cmB) 20 cm, 100 cmC) 10 cm, 50 cmD) None of these
Explanation:10 cm has been hammered in 0.5 cm then10 cm / 0.5 cm = 20.So the smaller side will be 20 and the ratio of 1:5 becomes 20:100.
Q4. 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?
A) 78 km/hB) 72 km/hC) 66 km/hD) 81 km/h
Explanation:If the length (in km) and speed (in km) of the train is L and St resp. We haveL / (St – 4.5) = 8.4/3600 andL/(St-5.4) = 8.5/3600Thus we get two equations,3600 L = 8.4 St – 54 and3600 L = 8.5 St – 45.9On Equating, we get 0.1St = 8.1St= Speed of train = 81
Q5. 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?
A) 12B) 36/5C) 60D) 20
Explanation:90 km/h = 90 x 5/18 m/s = 25 m/s.60 km/h = 60 x 5/18 m/s = 50/3 m/sT = D / S = (300+200) / (25 + 50/3) = 12 m/s.
Q6. 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
A) Rs.2800B) Rs.3600C) Rs.3300D) Rs.4800
Explanation:For enrolling in three activities = Rs.1075For enrolling in two activities = Rs.950So increase of Rs.125 for 1 more activity.Thus, for enrolling in four activities = Rs.1200So for three students enrolling in four activities= 3 x Rs 1200 = Rs 3600
Q7. 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?
A) 1205B) 949C) 1136D) 1075
Explanation:Total votes = 9801But 126 votes were invalid.Effective votes are 9675So total votes are distributed as 5x + 4x = 96759x = 9675 => x = 1075.
Q8. 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
A) 25 hoursB) 10 hoursC) 15 hoursD) 15/4 hours
Explanation:Two water taps together can fill a tank in 75/3 hrs.1/(x -10) + 1/x = 8/75 => x =15/4 or 100/4Smaller tap can fill the tank separately in 25 hours.
Q9. 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?
A) 1/2 mB) 2 mC) 1 mD) 4 m
Explanation:The area of garden is 144πAnd the area of swimming pool is 25πShe extends the radius by r.Now the new radius of garden = 12 + r=> area = π(12 + r)2So, π(12 + r)2 – 25 π = 144π => (12 + r)2 = 169=> r = 1
Q10. 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?
A) 350kgB) 300kgC) 50kgD) 325kg
(X x 57.5 + 75 x 45) / (X + 75) = 55x = 300 kg.