(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 $p_2$?
If $\oplus \div \odot = 2$, $\oplus \div \triangle = 3$, $\odot + \triangle = 5$, and $\Delta \times \otimes = 10$,
then the value of $(\otimes - \oplus)^2$ is:- The remainder when $98!$ is divided by $101$ is equal to ________
- 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 ________.
