Ramu can reach a certain place in 30 hours. If he reduces his speed by \( \frac{1}{15} \)th, he goes 10 km less in that time. Find his speed.
This problem involves concepts of speed, distance, and time. We are given the time taken and a reduction in speed, which leads to a reduction in distance covered. We can set up equations based on the formula \(\text{Distance} = \text{Speed} \times \text{Time}\) to find the original speed.
Let Ramu's original speed be \(S\) km/h and the original distance be \(D\) km.
We are given that Ramu can reach a certain place in 30 hours. So, using the formula \(\text{Distance} = \text{Speed} \times \text{Time}\):
\[ D = S \times 30 \quad \text{(Equation 1)} \]If he reduces his speed by \( \frac{1}{15} \)th, his new speed will be:
\[ S_{\text{new}} = S - \frac{1}{15}S = S \left(1 - \frac{1}{15}\right) = S \left(\frac{14}{15}\right) \text{ km/h} \]In the same time (30 hours), he goes 10 km less. So, the new distance covered is \((D - 10)\) km.
Using the new speed and new distance with the same time:
\[ D - 10 = S_{\text{new}} \times 30 \]\[ D - 10 = \left(\frac{14}{15}S\right) \times 30 \quad \text{(Equation 2)} \]Now we have a system of two equations:
Equation 1: \(D = 30S\)
Equation 2: \(D - 10 = 28S\)
Substitute Equation 1 into Equation 2:
\[ 30S - 10 = 28S \]Solve for \(S\):
\[ 30S - 28S = 10 \]\[ 2S = 10 \]\[ S = \frac{10}{2} \]\[ S = 5 \text{ km/h} \]D) 5 km/h is the original speed of Ramu.
India's Polar Satellite Launch Vehicle (PSLV-C45) successfully launched _____ on 1st April, 2019.
The question asks to identify the satellite successfully launched by ISRO's PSLV-C45 on April 1, 2019. This requires knowledge of specific ISRO missions and their payloads.
Correct Option: C) EMISAT
This is a blood relation problem. We need to decode the relationship described in the statement step-by-step, starting from the end of the phrase and working backward to establish the connection between Sujeeta and Radha.
The statement is: "Radha's maternal grandmother's only son-in-law is Sujeeta's father."
Let's break down the relationship from Radha's perspective:
Now, let's connect this to Sujeeta:
If Radha's father is Sujeeta's father, it means Radha and Sujeeta share the same father. This makes them siblings.
Thus, Sujeeta is Radha's sister.
B) Sister — As derived from the step-by-step analysis, Radha's father is also Sujeeta's father, making them sisters.
The following figure is a combination of 4 figures, A, B, C and D. Figure A represents people who are pizza lovers while figure B represents burger lovers. Figure C and D represent noodle and dumpling lovers respectively. According to the figure below, what does region 5 depict?
People who are only pizza and dumpling lovers
People who are pizza, noodle and dumpling lovers
People who are pizza, noodle and burger lovers
People who are only pizza and noodle lovers
The diagram is a Venn diagram representing different groups of food lovers. Each figure represents a different group: pizza, burger, noodle, and dumpling lovers. The regions where these figures overlap indicate people who love multiple types of food.
Correct Option: B) People who are pizza, noodle and dumpling lovers
Simplify the following.
\( \frac{2}{5} \)× [2 + {3 + (12 + 4 + 3)}]
9 \( \frac{3}{2} \)
9 \( \frac{3}{4} \)
9 \( \frac{3}{6} \)
9 \( \frac{3}{5} \)
To simplify the given expression, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This means we first solve operations inside Brackets/Parentheses, then Orders/Exponents, then Division and Multiplication (from left to right), and finally Addition and Subtraction (from left to right).
D) \( 9 \frac{3}{5} \) is the correct simplification of the given expression, as derived through the step-by-step process.
This problem involves tracking Karan's movement in different directions and calculating his final position relative to his starting point. We can solve this by breaking down his movements into North-South and East-West components.
Let's summarize the movements in terms of North/South and East/West components:
Total North-South displacement: \(100 + 40 - 140 = 140 - 140 = 0\) steps.
Total East-West displacement: \(-30 + 40 = 10\) steps.
Since the net North-South displacement is 0, Karan is neither North nor South of his starting point. The net East-West displacement is +10 steps, which means he is 10 steps to the East of his starting point.
A) 10 steps, East. As calculated, Karan's final position is 10 steps to the East of his starting point.
Solve the following
\(\sqrt[3]{\sqrt{0.000064}}\)= ?
To solve this problem, we need to evaluate the given expression by first calculating the square root of the decimal number and then finding the cube root of the result. It's helpful to convert the decimal to a fraction to simplify the root calculations.
The number inside the square root is \(0.000064\). This can be written as:
\[ 0.000064 = \frac{64}{1000000} \]Now, find the square root of this fraction:
\[ \sqrt{0.000064} = \sqrt{\frac{64}{1000000}} = \frac{\sqrt{64}}{\sqrt{1000000}} \]We know that \(\sqrt{64} = 8\) and \(\sqrt{1000000} = \sqrt{10^6} = 10^3 = 1000\). So,
\[ \sqrt{0.000064} = \frac{8}{1000} = 0.008 \]Now we need to find the cube root of the result from step 2, which is \(0.008\):
\[ \sqrt[3]{0.008} \]Again, convert the decimal to a fraction:
\[ 0.008 = \frac{8}{1000} \]So, the expression becomes:
\[ \sqrt[3]{\frac{8}{1000}} = \frac{\sqrt[3]{8}}{\sqrt[3]{1000}} \]We know that \(\sqrt[3]{8} = 2\) (since \(2 \times 2 \times 2 = 8\)) and \(\sqrt[3]{1000} = 10\) (since \(10 \times 10 \times 10 = 1000\)).
Therefore,
\[ \sqrt[3]{0.008} = \frac{2}{10} = 0.2 \]Thus, \(\sqrt[3]{\sqrt{0.000064}} = 0.2\).
A) 0.2
We are given the ratio of the current ages of Naresh and Suresh and the sum of their current ages. We need to find the ratio of their ages after 15 years. First, we will use the given ratio and sum to find their current individual ages. Then, we will add 15 years to each of their current ages to find their ages after 15 years and finally calculate the new ratio.
Let the current age of Naresh be \(6x\) years and the current age of Suresh be \(5x\) years, based on the given ratio of 6:5.
The sum of their current ages is given as 44 years. So, we can write the equation:
\[ 6x + 5x = 44 \]Combine the terms to solve for \(x\):
\[ 11x = 44 \]\[ x = \frac{44}{11} \]\[ x = 4 \]Now, calculate their current individual ages:
Next, calculate their ages after 15 years:
Finally, find the ratio of their ages after 15 years:
\[ \text{Ratio} = \frac{\text{Age of Naresh after 15 years}}{\text{Age of Suresh after 15 years}} = \frac{39}{35} \]The ratio of their respective ages after 15 years will be 39 : 35.
Correct Option: A) 39 : 35
The question asks about the primary physical quantity that a spring balance is designed to measure. We need to recall the working principle of a spring balance and the definitions of the given options.
Correct Option: A) force
A spring balance measures the force applied to it. When an object is hung from it, the force measured is the gravitational force acting on the object, which is its weight. Thus, 'force' is the more general and accurate answer.
The question asks for the scientific name of Muriatic acid. This requires knowledge of common names for chemical compounds, specifically acids.
C) Hydrochloric acid
Muriatic acid is the traditional and common name for hydrochloric acid (\(\text{HCl}\)). It is often used to refer to a dilute, impure form of hydrochloric acid, particularly for industrial or household applications like cleaning masonry, adjusting pH in swimming pools, and pickling steel.