Simplification-Test 8 (Based on Algebraic formulae/Statement simplifications)

Answer: Option B

Explanation

Let shailesh's monthly income be Rs. x,

$\begin{array}{l}\text{Mehul's monthly income}=Rs\frac{15x}{8}\\ \\ \text{Prashant's monthly income}=Rs\frac{15x}{8}\\ \\ \therefore x+\frac{3x}{2}+\frac{15x}{8}=183750\\ \\ \Rightarrow \frac{8x+12x+15x}{8}=183750\\ \\ \Rightarrow \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}35}x\text{ = 183750}\times \text{8}\\ \\ \Rightarrow x=\frac{\text{183750}\times \text{8}}{35}\text{ = Rs 42000}\\ \\ \therefore \text{ Prashant's monthly income}\\ \\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}=Rs}(\frac{15}{8}\times 42000)=Rs78750\end{array}$

Hence, option B is correct.

Answer: Option A

Explanation

$$\begin{gathered} \begin{array}{l}\text{Here, number of extra sweets}\\ \\ \text{ = 2}\times \text{480 = 960}\\ \\ \text{These sweets were to be distributed}\\ \text{among 120 children.}\\ \\ \therefore \text{ Number of sweets to be given to each}\\ \text{child on originally = }\frac{\text{960}}{120}\text{ = 8}\end{array} \\ Hence, option A is correct. \end{gathered}$$

Answer: Option C

Explanation

$$\begin{gathered} \begin{array}{l}\text{Let the number of hens be }x\text{ and that of}\\ \text{goats bey.}\\ \\ \therefore x+y=\text{90 ----(i)}\\ \\ 2x+4y=248\\ \\ \Rightarrow x+2y=124\\ \\ \Rightarrow \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em} 90}-\text{y + 2y = 124 [from Eq. (i)]}\\ \\ \Rightarrow y=124-90=34\end{array} \\ Hence, option C is correct. \end{gathered}$$

Answer: Option C

Explanation

$\begin{array}{l}\text{Here, cost of 8 kg of apples}\\ \\ =\frac{450}{5}\times 8=Rs750\\ \\ \text{Here, cost of 8 kg of apples}\\ \\ =\frac{4320}{12}\times 8\\ \\ =Rs2880\\ \\ \text{Cost of 8 kg of oranges}\\ \\ =\frac{240}{4}\times 8\\ \\ =Rs480\\ \\ \therefore \text{Total cost=Rs (720 + 2880 + 480)}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}= Rs 4080}\end{array}$

Hence, option C is correct.

Answer: Option C

Explanation

$\begin{array}{l}\text{Here, total cost of 15 chappattis}\\ \\ \text{= 15}\times \text{5= Rs 75}\\ \\ \text{Total cost of 4 plates of rice}\\ \\ \text{= 4}\times \text{50}\\ \\ \text{=200}\\ \\ \text{Total cost of 6 plates of mixed vegetables}\\ \\ \text{= 6}\times \text{75}\\ \\ \text{= Rs 450}\\ \\ \text{Total cost of 5 ice-creams}\\ \\ \text{= 5}\times \text{20}\\ \\ \text{= Rs 100}\\ \\ \therefore \text{ Total amount pair by Arun}\\ \\ \text{= 75 + 200 + 450 + 100}\\ \\ \text{=Rs 825}\end{array}$

Hence, option C is correct.