(Answer in integer)
Lions and Tigers Food Calculation
This problem requires setting up and solving a system of linear equations to determine the weekly food consumption of a single lion.
Setting Up the Equations
Let $L$ represent the amount of food (in kg) a single lion eats per week, and $T$ represent the amount of food (in kg) a single tiger eats per week.
- Zoo 1: 3 lions and 4 tigers eat 390 kg.
Equation 1: $3L + 4T = 390$ - Zoo 2: 4 lions and 5 tigers eat 500 kg.
Equation 2: $4L + 5T = 500$
Solving the System of Equations
We can use the elimination method to solve for $L$.
- Multiply Equation 1 by 4 and Equation 2 by 3 to make the coefficients of $L$ the same:
- $4 \times (3L + 4T = 390) \implies 12L + 16T = 1560$
- $3 \times (4L + 5T = 500) \implies 12L + 15T = 1500$
- Subtract the second modified equation from the first to eliminate $L$:
$(12L + 16T) - (12L + 15T) = 1560 - 1500$
$T = 60$ - Substitute the value of $T$ (60) back into Equation 1 to find $L$:
$3L + 4(60) = 390$
$3L + 240 = 390$
$3L = 390 - 240$
$3L = 150$
$L = \frac{150}{3}$
$L = 50$
Lion's Weekly Food Intake
The amount of food a single lion eats per week is 50 kg.
Important Questions from Numerical Reasoning
- Let $p_1$ and $p_2$ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of $p_1$ and $p_2$?
- A 'frabjous' number is defined as a 3 digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous number, while 133 is not. How many such frabjous numbers exist?
Ankita has to climb 5 stairs starting at the ground, while respecting the following rules:
1. At any stage, Ankita can move either one or two stairs up.
2. At any stage, Ankita cannot move to a lower step.
Let $F(N)$ denote the number of possible ways in which Ankita can reach the $N^{th}$ stair. For example, $F(1) = 1$, $F(2) = 2$, $F(3) = 3$. The value of $F(5)$ is ________.Consider a spherical globe rotating about an axis passing through its poles. There are three points P, Q, and R situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let P, Q, and R move with speeds $v_P$, $v_Q$, and $v_R$, respectively.
Which one of the following options is CORRECT?
A dozer pushes up a 100 kg spool of cable along a $20^ \circ$ incline road at a constant velocity as shown in the figure. The figure shows a dozer pushing a spool (diameter 400 mm) up a $20^ \circ$ incline. Point A is the contact point between the spool and the road, and Point B is the contact point between the dozer bucket and the spool. The coefficient of static friction between the dozer bucket and the spool (Point B) is 0.45, and coefficient of kinetic friction between road and the spool (Point A) is 0.15.
Consider the spool only slides up the incline. The maximum normal force in N acting at Point B, is ___________ [rounded off to 1 decimal place]
