1. How many Kg of rice at Rs.6.60 per Kg. be mixed with 56Kg of rice at Rs.9.60 per Kg to get a mixture worth Rs.8.20 per Kg
A. 56 Kg
B. 52 Kg
C. 44 Kg
D. 49 Kg
E. None of these
2. How many litres of water must be added to 16 liters of milk and water contains 10% water to make it 20% water in it
A. 4 litre
B. 2 litre
C. 1 litre
D. 3 litre
E. None of these
3. We have a 630 ml of mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?
A. 70 ml
B. 60 ml
C. 80 ml
D. 50 ml
E. None of these
4. 3 litre of water is added to 11 litre of a solution containing 42% of alcohol in the water. The percentage of alcohol in the new mixture is
A. 25%
B. 20%
C. 30%
D. 33%
E. None of these
5. Rs.460 was divided among 41 boys and girls such that each boy Rs.12 and each girl got Rs.8. What is the number of boys?
A. 33
B. 30
C. 36
D. 28
E. None of these
6.If the difference between the simple interest and compound interests on some principal amount at 20% for 3 years is Rs. 48, then the principal amount is
A. Rs. 365
B. Rs. 325
C. Rs. 395
D. Rs. 375
E. None of these
7.A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present
A. 38
B. 40
C. 42
D. 44
E. None of these
8.30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years?
A. 60%
B. 70%
C. 80%
D. 90%
E. None of these
9. Pipes A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in.
A. 3 9/5
B. 3 9/17
C. 3 7/5
D. 3 7/17
E. None of these
10. A clock is started at noon. By 10 minutes past 5, the hour hand has turned through
A. 155°
B. 145°
C. 152°
D. 140°
E. None of these
ANSWERS AND SOLUTION:
1 (D)Explanation :
By the rule of alligation, we have
Cost of 1 kg of 1st kind rice Cost of 1 kg of 2nd kind rice
6.6 9.6
Price of 1Kg of the mixture
8.2
9.6 - 8.2 = 1.4 8.2 - 6.6 = 1.6
Quantity of 1st kind rice : Quantity of 2nd kind rice = 1.4 : 1.6 = 7 : 8
Quantity of 1st kind rice : 56 = 7 : 8
=>Quantity of 1st kind rice = 56×7/8=49
2 (B)Explanation :By the rule of alligation, we have
% Concentration of water % Concentration of water
in pure water : 100 in the given mixture :
Mean % concentration
20
20 - 10 = 10 100 - 20 = 80
=> Quantity of water : Quantity of the mixture = 10 : 80 = 1 : 8
Here Quantity of the mixture = 16 litres
=> Quantity of water : 16 = 1 : 8
Quantity of water = 16×1/8=2 litre
3 (A)Explanation :
concentration of water in mixture1 = 2/9 (Since the ratio of milk and water = 7:2) ---item(1)
concentration of water in pure water= 1 ---item(2)
Now the above mentioned items are mixed to form a mixture2 where milk and water ratio = 7: 3
=>concentration of water in mixture2 = 3/10
By the rule of alligation, we have
concentration of water concentration of water
in mixture1 : 2/9 in pure water : 1
Mean concentration
3/10
1 - 3/10 = 7/10 3/10 - 2/9 = 7/90
=> Quantity of mixture1 : Quantity of water = 7/10 : 7/90 = 1/10 : 1/90 = 1 : 1/9
Given that Quantity of mixture1 = 630 ml
=> 630 : Quantity of water = 1 : 1/9
=Quantity of water = 630×19=70 ml
4 (D)Explanation :
%Concentration of alcohol in pure water = 0
%Concentration of alcohol in mixture = 42
quantity of water : Quantity of mixture = 3 : 11
Let the %Concentration of alcohol in the new mixture = x
By the rule of alligation, we have
%Concentration of alcohol : 0 %Concentration of alcohoI
in pure water in mixture : 42
Mean %Concentration
x
42 - x x - 0 = x
But (42 - x) : x = 3 : 11
=42-x/x = 3/11
=42×11-11x = 3x
=14x = 42×11
=x=3×11 = 33
=> The percentage of alcohol in the new mixture is 33%
5 (A)Explanation :Let that the number of boys = b and number of girls is g
number of boys + number of girls = 41
=> b + g = 41 ------------ (Equation 1)
Given that each boy got Rs.12 and each girl got Rs.8 and Total amount = Rs.460
=> 12b + 8g = 460 -------- (Equation 2)
Now we need solve Equation 1 and Equation 2 to get b and g
(Equation1)×8=>8b+8g=8×41=328--------(Equation3)
(Equation 2) - (Equation 3) = 4b = 460 - 328 = 132
=>b=132/4=33
6 (D)Explanation : Let the sum be Rs.x
Amount after 3 years on Rs.x at 20% per annum when interest is compounded annually
=P(1+R/100)^T=x(1+20/100)^3=x(120/100)^3=x(6/5)^3
Compound Interest = x(6/5)^3-x = x[(6/5)^3-1] =x[216/125-1]=91x/125
Simple Interest = PRT/100=x×20×3/100 =3x/5
Given that difference between compound interest and simple interest is Rs.48
91x/125-3x/5=48
(91x-75x)/125=48
16x/125=48
x=48×125/16 =3×125= Rs. 375
i.e, the sum is Rs.375
7 (B)Explanation:Let the mother's present age be x years.
Then, the person's present age = (2/5 x) years.
=> (2/5 x + 8/2) = 1 (x + 8)
=> 2(2x + 40) = 5(x + 8)
=> x = 40
8 (C)Explanation :Let total number of men = 100
Then, 80 men are less than or equal to 50 years old
(Since 80% of the men are less than or equal to 50 years old)
=> 20 men are above 50 years old (Since we assumed total number of men as 100)
=>20% of the men above the age of 50 play football
?Number of men above the age of 50 who play football = 20×20/100=4
Number of men who play football = 20 (Since 20% of all men play football)
Percentage of men who play football above the age of 50 = 4/20×100=20%
=>Percentage of men who play football less than or equal to the age 50 = 100%-20%=80%
9 (B)Explanation:
Net part filled in 1 hour = (1/5+1/6-1/12)
=17/60hrs
=3 9/17
10 (A)Explanation :We know that Angle traced by hour hand in 12 hrs = 360°
Time duration from noon to 10 minutes past 5 = 5 hours 10 minutes
=5 10/60hour =31/6 hours
Hence the angle traced by hour hand from noon to 10 minutes past 5 = 31/6×360/12 =31/6×30=31×5=155°
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