Q1)-An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:
Q2)-The train 'A' leaves station P at 5 a.m. and reaches station Q at 9 a.m. Another train 'B' leaves station Q at 7 am and reaches station P at 10:30 am. At what time do the two trains cross each other?
Q3)-The letter of the word ASSASSIN are written down at random in a row. The probability that no two 'S' occur together is:
Q4)-Free pencils were distributed equally among children of a class. The number of pencils each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 pencils. How many pencils were distributed in all?
Q5)-Five litres of water is added to a certain quantity of pure milk costing Rs 3 per litre. If by selling the mixture at the same price as before, a profit of 20% is made, what is the amount of pure milk in the mixture?
Q6)-There were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increased by Rs 42 per day while the average expenditure per head reduced by Rs 1. Find the original expenditure of the mess.
Q7)-Two casks of 48 L and 42 L are filled with mixtures of milk and water. The proportions in the two casks being respectively 13 : 7 and 18 : 17. If the contents of the two casks be mixed and 20 L of water be added to the whole, what will be the proportion of milk and water in the resulting mixture?
Q8)-A certain factory employed 600 men and 400 women and the average wage was Rs 2.55 per day. If a woman got 50 paisa less than a man, what was the daily wage of a woman worker?
Q9)-72% of 390 + 28% of 165 = ? + 3
Q10)-12 men went to a restaurant, 11 of them spent Rs 50 each and the 12th person spent Rs. 110 more than the average expenditure of all. Find the total money spent by them.
10%
10.25%
10.5%
15.25%
Ans.- B
Let the sum be Rs. 100. Then,
Simple Interest for the first 6 months = Rs [100 * 10 * (1/2)]/100 = Rs 5
Principal for the last 6 months = Rs(100 + 5) = Rs 105
Simple Interest for the last 6 months = Rs [105 * 10 * (1/2)]/100 = Rs 5.25
So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25
.'. Effective rate of interest = (110.25 - 100)% = 10.25%
Let the sum be Rs. 100. Then,
Simple Interest for the first 6 months = Rs [100 * 10 * (1/2)]/100 = Rs 5
Principal for the last 6 months = Rs(100 + 5) = Rs 105
Simple Interest for the last 6 months = Rs [105 * 10 * (1/2)]/100 = Rs 5.25
So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25
.'. Effective rate of interest = (110.25 - 100)% = 10.25%
Q2)-The train 'A' leaves station P at 5 a.m. and reaches station Q at 9 a.m. Another train 'B' leaves station Q at 7 am and reaches station P at 10:30 am. At what time do the two trains cross each other?
7 : 36 am
7 : 56 am
8 : 36 am
8 : 56 am
Ans.- B
Let the distance between P and Q be x km.
Time taken by A to cover the distance PQ = 4 hours
Time taken by B to cover the distance PQ = 3 hours 30 minutes = 7/2 hours
Then, The speed of train A = x/4 km/h
And, the speed of train B = x/(7/2) = 2x/7 km/h
So, relative speeds of the trains = (x/4 + 2x/7) = 15x/28 km/h
Now, distance covered by Train A in 2 hours = x/4 * 2 = x/2 km
Distance between trains A and B at 7 am = x - x/2 = x/2 km
Time taken to cross each other = (x/2)/(15x/28) = 14/15 hours = 14/15 * 60 = 56 minutes.
Hence, both trains cross each other at 7 : 56 am.
Let the distance between P and Q be x km.
Time taken by A to cover the distance PQ = 4 hours
Time taken by B to cover the distance PQ = 3 hours 30 minutes = 7/2 hours
Then, The speed of train A = x/4 km/h
And, the speed of train B = x/(7/2) = 2x/7 km/h
So, relative speeds of the trains = (x/4 + 2x/7) = 15x/28 km/h
Now, distance covered by Train A in 2 hours = x/4 * 2 = x/2 km
Distance between trains A and B at 7 am = x - x/2 = x/2 km
Time taken to cross each other = (x/2)/(15x/28) = 14/15 hours = 14/15 * 60 = 56 minutes.
Hence, both trains cross each other at 7 : 56 am.
Q3)-The letter of the word ASSASSIN are written down at random in a row. The probability that no two 'S' occur together is:
1/35
1/14
1/15
1/22
Ans.- B
Q4)-Free pencils were distributed equally among children of a class. The number of pencils each child got was one-eighth of the number of children. Had the number of children been half, each child would have got 16 pencils. How many pencils were distributed in all?
432
640
512
625
Ans.- C
Q5)-Five litres of water is added to a certain quantity of pure milk costing Rs 3 per litre. If by selling the mixture at the same price as before, a profit of 20% is made, what is the amount of pure milk in the mixture?
25 litres
20 litres
15 litres
30 litres
Ans.- A
Here, cost price of water = Rs 0
And, Profit% = 20 %
So, selling price of the mixture = cost price of pure milk.
=> 120/100 * cost price of mixture = 3
=> Cost price of mixture = 3 * 100/120 = Rs 2.5 per litre
Here, cost price of water = Rs 0
And, Profit% = 20 %
So, selling price of the mixture = cost price of pure milk.
=> 120/100 * cost price of mixture = 3
=> Cost price of mixture = 3 * 100/120 = Rs 2.5 per litre
Q6)-There were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increased by Rs 42 per day while the average expenditure per head reduced by Rs 1. Find the original expenditure of the mess.
Rs 420
Rs 450
Rs 300
Rs 400
Ans.- A
Let the average expenditure per day was Rs x. Then,
The total expenditure per day = 35x.
When 7 more students join the mess, total expenditure per day = 35x + 42
Now, the average expenditure = (35x + 42)/(35 + 7) = (35x + 42)/42
Then, (35x + 42)/42 = x - 1
=> 35x + 42 = 42x – 42
=> 7x = 84
=> x = 12
Thus the original expenditure of the mess = 35 * 12 = Rs 420.
Let the average expenditure per day was Rs x. Then,
The total expenditure per day = 35x.
When 7 more students join the mess, total expenditure per day = 35x + 42
Now, the average expenditure = (35x + 42)/(35 + 7) = (35x + 42)/42
Then, (35x + 42)/42 = x - 1
=> 35x + 42 = 42x – 42
=> 7x = 84
=> x = 12
Thus the original expenditure of the mess = 35 * 12 = Rs 420.
Q7)-Two casks of 48 L and 42 L are filled with mixtures of milk and water. The proportions in the two casks being respectively 13 : 7 and 18 : 17. If the contents of the two casks be mixed and 20 L of water be added to the whole, what will be the proportion of milk and water in the resulting mixture?
5 : 12
7 : 13
12 : 13
8 : 14
Ans.- C
Q8)-A certain factory employed 600 men and 400 women and the average wage was Rs 2.55 per day. If a woman got 50 paisa less than a man, what was the daily wage of a woman worker?
Rs 2.75
Rs. 3.25
Rs 3
Rs 2.25
Ans.- D
Total number of workers = 600 + 400 = 1000
Total wages per day = 2.55 * 1000 = Rs 2550
Let Rs 'x' be the daily wage of a man worker.
Then, 600x + 400(x - 0.50) = 2550
=> 600x + 400x – 200 = 2550
=> 1000x = 2750
=> x = 2.75
Daily wage of a woman worker = Rs (2.75 – 0.50) = Rs 2.25
Total number of workers = 600 + 400 = 1000
Total wages per day = 2.55 * 1000 = Rs 2550
Let Rs 'x' be the daily wage of a man worker.
Then, 600x + 400(x - 0.50) = 2550
=> 600x + 400x – 200 = 2550
=> 1000x = 2750
=> x = 2.75
Daily wage of a woman worker = Rs (2.75 – 0.50) = Rs 2.25
Q9)-72% of 390 + 28% of 165 = ? + 3
328
324
331
322
Ans.- B
72% of 390 + 28% of 165 = ? + 3
=> 72/100 * 390 + 28/100 * 165 = ? + 3
=> 280.8 + 46.2 = ? + 3
=> ? = 327 – 3 = 324
72% of 390 + 28% of 165 = ? + 3
=> 72/100 * 390 + 28/100 * 165 = ? + 3
=> 280.8 + 46.2 = ? + 3
=> ? = 327 – 3 = 324
Q10)-12 men went to a restaurant, 11 of them spent Rs 50 each and the 12th person spent Rs. 110 more than the average expenditure of all. Find the total money spent by them.
Rs 640
Rs 720
Rs 560
Rs 840
Ans.- B
Let the average money spent by all 12 men be Rs. x.
And, money spent by the 12th men = Rs (x + 110)
Money spent by remaining 11 men = Rs (50 * 11) = Rs 550
According to the question, (x + 110 + 550)/12 = x
=> 12x = x + 660
=> 11x = 660
=> x = 60
Total money spent by 12 men = Rs. (12 * 60) = Rs 720
Let the average money spent by all 12 men be Rs. x.
And, money spent by the 12th men = Rs (x + 110)
Money spent by remaining 11 men = Rs (50 * 11) = Rs 550
According to the question, (x + 110 + 550)/12 = x
=> 12x = x + 660
=> 11x = 660
=> x = 60
Total money spent by 12 men = Rs. (12 * 60) = Rs 720
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