Answer :
Let's go through each question step-by-step:
Q 46: Probability of getting the product of 30 on two fair dice rolled.
When rolling two six-sided dice, the possible outcomes for each die are 1, 2, 3, 4, 5, and 6. The total number of outcomes is [tex]6 \times 6 = 36[/tex].
To find when the product of the numbers on the dice is 30, consider the factors of 30 that can be rolled:
- Possible factor pairs that could result in a product of 30 are (1, 30), (2, 15), (3, 10), (5, 6), and (6, 5).
- However, since each die can only have numbers 1 through 6, the only possible pair is (5, 6) or (6, 5).
Thus, there are 2 favorable outcomes where the product is 30.
Therefore, the probability is [tex]\frac{2}{36} = \frac{1}{18}[/tex].
Answer: C. [tex]\frac{1}{18}[/tex]
Q 47: Capacity of the tank with two pipes and a leak.
- Pipe 1 fills the tank in 36 minutes, so it fills [tex]\frac{1}{36}[/tex] of the tank per minute.
- Pipe 2 fills the tank in 30 minutes, so it fills [tex]\frac{1}{30}[/tex] of the tank per minute.
Both pipes together fill [tex]\frac{1}{36} + \frac{1}{30} = \frac{5}{180} + \frac{6}{180} = \frac{11}{180}[/tex] of the tank per minute.
With both pipes open, the tank is filled in 15 minutes:
- The effective filling rate with both pipes and the leak is [tex]\frac{1}{15}[/tex] of the tank per minute.
The rate at which the leak drains the tank is [tex]\frac{24}{x}[/tex], where [tex]x[/tex] is the capacity of the tank in liters. The effective fill rate is:
- [tex]\frac{11}{180} - \frac{24}{x} = \frac{1}{15}[/tex]
To find [tex]x[/tex], solve:
[tex]\frac{11}{180} - \frac{24}{x} = \frac{1}{15}[/tex]
Multiply through by [tex]180x[/tex] to clear fractions:
[tex]11x - 24 \times 180 = 180x/15[/tex]
This simplifies to [tex]11x - 4320 = 12x[/tex].
Thus, [tex]x = 4320[/tex].
Answer: A. 4320 liters
Q 48: Ratios of distances driven by Robert and Donald.
- Robert’s distance [tex]D_1[/tex] = speed [tex]\times[/tex] time = [tex]75 \times 9 = 675[/tex] km.
- Donald’s distance [tex]D_2[/tex] = speed [tex]\times[/tex] time = [tex]60 \times 7.25 = 435[/tex] km.
The ratio is [tex]\frac{675}{435} = \frac{45}{29}[/tex].
Answer: A. 45: 29
Q 49: Usual time taken by person driving to office.
Let the usual time be [tex]t[/tex] hours.
- Usual distance [tex]= 40t[/tex].
- Driving at 45 km/hr, he covers the same distance in [tex](t - \frac{1}{6})[/tex] hours.
Equating the distance:
[tex]40t = 45(t - \frac{1}{6})[/tex]
Solving:
[tex]40t = 45t - 7.5[/tex]
[tex]5t = 7.5[/tex]
[tex]t = 1.5[/tex] hours, or 90 minutes.
Answer: A. 90 minutes
Q 50: New ratio of Kia Seltos and Volkswagen Vento prices.
Let the prices of Kia Seltos and Volkswagen Vento be [tex]11x[/tex] and [tex]12x[/tex] respectively.
- After a 20% increase in Kia Seltos: Price = [tex]11x \times 1.2 = 13.2x[/tex].
- After a 25% increase in Volkswagen Vento: Price = [tex]12x \times 1.25 = 15x[/tex].
The new ratio is [tex]\frac{13.2}{15} = \frac{22}{25}[/tex].
Answer: A. 22:25
