Toffee Fraction Word Problem Solution
This problem requires us to determine the initial quantity of toffees by reversing the actions described, starting from the final count.
Working Backward Solution Steps
- Final State: There are 17 toffees remaining in the bowl.
- Reverse T's Action: T returned 2 toffees. Before returning them, the count was $17 + 2 = 19$. T had taken half the available toffees ($N_T$) before returning 2. This means the $19$ toffees represent the half T didn't take plus the 2 returned. Let $N_T$ be the number of toffees before T took his share. T took $N_T / 2$. The amount remaining after T took his share was $N_T - N_T / 2 = N_T / 2$. After returning 2, the amount became $N_T / 2 + 2$. We know this equals 17.
So, $\frac{N_T}{2} + 2 = 17$.
Solving for $N_T$:
$\frac{N_T}{2} = 17 - 2$
$\frac{N_T}{2} = 15$
$N_T = 15 \times 2 = 30$. This means 30 toffees were present after S finished his actions. - Reverse S's Action: S returned 3 toffees. Before returning them, the count was $30 + 3 = 33$. S had taken $1/4^{th}$ of the available toffees ($N_S$) before returning 3. The amount left after S took his share was $N_S - \frac{N_S}{4} = \frac{3N_S}{4}$. After returning 3, the amount became $\frac{3N_S}{4} + 3$. We know this equals 30.
So, $\frac{3N_S}{4} + 3 = 30$.
Solving for $N_S$:
$\frac{3N_S}{4} = 30 - 3$
$\frac{3N_S}{4} = 27$
$N_S = 27 \times \frac{4}{3} = 9 \times 4 = 36$. This means 36 toffees were present after R finished his actions. - Reverse R's Action: R returned 4 toffees. Before returning them, the count was $36 + 4 = 40$. R had taken $1/3^{rd}$ of the original toffees ($N_0$) before returning 4. The amount left after R took his share was $N_0 - \frac{N_0}{3} = \frac{2N_0}{3}$. After returning 4, the amount became $\frac{2N_0}{3} + 4$. We know this equals 36.
So, $\frac{2N_0}{3} + 4 = 36$.
Solving for $N_0$:
$\frac{2N_0}{3} = 36 - 4$
$\frac{2N_0}{3} = 32$
$N_0 = 32 \times \frac{3}{2} = 16 \times 3 = 48$.
Original Toffee Calculation
The original number of toffees in the bowl was 48.
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 ________.- In a zoo, three lions and four tigers eat 390 kg of food every week. In another zoo, four lions and five tigers eat 500 kg of food every week. Lions and tigers eat different amounts of food, but all individuals of the same species eat the same amount. The amount of food a single lion eats per week is ________ kg.
(Answer in integer) 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?
