To solve the problem, let's define the prices and quantities of the different varieties of tea being mixed.
Given:
Let the price of the third variety of tea be x Rs./kg.
The total mixture is worth Rs. 153/kg. Since the ratio of the tea varieties is 1:1:2, we can assume the quantities of each type of tea in the mixture to be:
The total cost of the mixture can be expressed as the weighted average cost of the individual varieties based on their respective quantities.
Let's compute the cost per unit for the mixture:
The total quantity of the mixture is:
The average price per kg of the mixture is given as Rs. 153. Therefore, we set up the equation:
First, simplify the numerator:
Next, substitute this back into the equation and solve for x:
Multiply both sides by 4 to clear the denominator:
Now, isolate x:
Thus, the price of the third variety of tea is Rs. 175.50 per kg.
5% of A + 4% of B = | 2 | (6% of A + 8% of B) |
3 |
⟹ | 5 | A + | 4 | B | = | 2 | ❨ | 6 | A + | 8 | B | ❩ |
100 | 100 | 3 | 100 | 100 |
⟹ | 1 | A + | 1 | B | = | 1 | A + | 4 | B |
20 | 25 | 25 | 75 |
⟹ | ❨ | 1 | - | 1 | ❩ A = | ❨ | 4 | - | 1 | ❩ B |
20 | 25 | 75 | 25 |
⟹ | 1 | A = | 1 | B |
100 | 75 |
A | = | 100 | = | 4 | . |
B | 75 | 3 |
∴ Required ratio = 4 : 3
Speed = | ❨ | 240 | ❩m/sec = 10 m/sec. |
24 |
∴ Required time = | ❨ | 240 + 650 | ❩sec = 89 sec. |
10 |
Odd days in 1600 years = 0
Odd days in 300 years = (5 x 3) ≡ 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.
Jan. Feb. March April May June (31 + 28 + 31 + 30 + 31 + 17) = 168 days
∴ 168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.
Other number = | ❨ | 11 x 7700 | ❩ | = 308. |
275 |
Let 1872/?N = 234.
Then ?N = 1872/234 = 8
? N = 8 x 8 = 64
Let distance covered by dog in 1 leap is x and
Distance covered by cat in 1 leap is y
Then, 3x = 4y
? x= 4/3y
Now, Ratio of speed of dog and cat = Ratio of distance covered by them in the same time = 4x : 5y
= 16/3y : 5y
= 16 : 15
Total volume of cuboid = (10 x 5 x 2) cm3
= 100 cm3
Volume curved = 1/3 x (22/7) x 3 x 3 x 7 cm3
= 66 cm3
% of wood wasted = (100 - 66)% = 34 %
Series pattern
12, 32, 52, 72, 92, 112
So missing term = 112 = 121
Angle of 360° is covered by hour hand in 12 h .
So, angle of 135° is covered by hour hand in 12/360° x 135° = 4.5 h
Thus, required time = (3 + 4.5)h = 7.5 h = 7 : 30
Try yourself. It was Wednesday.
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