$X=$ Average profit amount of all items; $Y=$ Average discount amount of all items. Decide the relation between $X$ and $Y$.
$X=$ Average profit amount of all items; $Y=$ Average discount amount of all items. Decide the relation between $X$ and $Y$.
Show Hint
- If $X > Y$
- If $X < Y$
- If $X \geq Y$
If $X \leq Y$ or can't be determined
The Correct Option is B
Approach Solution - 1
Using the values computed in Q6:
Profits (SP–CP):
AC: ₹ \(50000-41666.\overline{6}=8333.\overline{3}\)
TV: ₹ \(36000-30000=6000\)
Cooler: ₹ \(15000-13636.\overline{36}=1363.\overline{63}\)
Mobile: ₹ \(31250-20833.\overline{3}=10416.\overline{6}\)
Laptop: ₹ \(75000-62500=12500\)
\[\text{Sum profit} = ₹38613.\overline{63}, \quad X = \frac{38613.\overline{63}}{5} \approx ₹7722.73\]
Discounts (MP–SP):
AC: ₹ \(62500-50000=12500\)
TV: ₹ \(60000-36000=24000\)
Cooler: ₹ \(18750-15000=3750\)
Mobile: ₹ \(41666.\overline{6}-31250=10416.\overline{6}\)
Laptop: ₹ \(107142.\overline{85}-75000=32142.\overline{85}\)
\[\text{Sum discount} \approx ₹82809.52, \quad Y = \frac{82809.52}{5} \approx ₹16561.90\]
Approach Solution -2
Instead of finding each item's profit and discount separately and then averaging, the totals can be built up directly from the aggregate cost price, selling price and marked price of all five items.
The cost prices are: T.V. \( ₹30000 \), A.C. \( ₹41666.67 \), Cooler \( ₹13636.36 \), Laptop \( ₹62500 \), Mobile \( ₹20833.33 \), giving a total cost price of \( ₹168636.36 \).
The selling prices are: T.V. \( ₹36000 \), A.C. \( ₹50000 \), Cooler \( ₹15000 \), Laptop \( ₹75000 \), Mobile \( ₹31250 \), giving a total selling price of \( ₹207250 \).
The marked prices are: T.V. \( ₹60000 \), A.C. \( ₹62500 \), Cooler \( ₹18750 \), Laptop \( ₹107142.86 \), Mobile \( ₹41666.67 \), giving a total marked price of \( ₹290059.53 \).
The total profit is \( 207250 - 168636.36 = ₹38613.64 \), so the average profit is \( X = \frac{38613.64}{5} = ₹7722.73 \). The total discount is \( 290059.53 - 207250 = ₹82809.53 \), so the average discount is \( Y = \frac{82809.53}{5} = ₹16561.91 \).
Now check each option:
- If \( X \gt Y \): This needs \( 7722.73 \gt 16561.91 \), which is false.
- If \( X \lt Y \): Since \( 7722.73 \lt 16561.91 \), this statement holds true.
- If \( X \geq Y \): This needs \( 7722.73 \geq 16561.91 \), which is false.
- If \( X \leq Y \) or can't be determined: Although \( X \leq Y \) is numerically true, the relation is fully determinable and is expressed more precisely by \( X \lt Y \), so this is not the best-fitting choice.
The relation that holds precisely is \( X \lt Y \).
So, the correct answer is If \( X \lt Y \).
Top SNAP Quantitative Aptitude Questions
- Rahul starts a business with ₹ 8000. After $6$ months, Sanjay joins with some capital. If their profits after one year are equal, find Sanjay's investment.
- A watch is bought for ₹ 1950 in cash and sold for ₹ 2200 on one-year credit. If the interest rate is $10\%$ p.a., find the trader's gain/loss.
- An article is listed at ₹ 65. A customer bought this article for ₹ 56.16 and got two successive discounts, the first being $10\%$. What was the other discount rate allowed by the shopkeeper?
A company has $50{,}000$ preferred shares with dividend $20\%$ and $20{,}000$ common shares; par value of each share is ₹ 10. The total profit is $₹ 1{,}80{,}000$, of which $₹ 30{,}000$ is kept in reserve and the rest distributed to shareholders. Find the dividend percent paid to common shareholders.
A man buys apples at a certain price per dozen and sells them at eight times that price per hundred. What is his gain or loss percent?
Top SNAP Average Questions
- Average stipend of a group is \rupee50 per day. The difference between maximum and minimum stipend is \rupee45. If both these students are excluded, the average decreases by \rupee1. The minimum earning of any student lies between \rupee42 and \rupee47, and the number of students is a prime number whose both digits are also prime. Find the initial number of students.
- A firm of readymade garments makes both men's and women's shirts. Its average profit is $6\%$ of the sales. Average profit in men's shirts is $8\%$ of the sales and women's shirts comprise $60\%$ of the output. The average profit per sale rupee in women's shirts is:
- The average of nine numbers is \(M\), and the average of three of these numbers is \(P\). If the average of the remaining six numbers is \(N\), which of the following must be true?
- The average of nine numbers is \(M\), and the average of three of these numbers is \(P\). If the average of the remaining six numbers is \(N\), which of the following must be true?
- If the algebraic sum of deviations of 20 observations measured from 23 is 70, what is the mean of these observations?
Top SNAP Questions
- In a retail outlet, the average revenue was Rs.10,000 per day over a 30 day period. During this period, the average revenue on weekends (total 8 days) was Rs. 20,000 per day. What was the average daily revenue on weekdays?
- Two different prime numbers X and Y, both are greater than 2, then which of the following must be true?
- It takes 6 hours for pump A, used alone, to fill a tank of water. Pump B alone takes 8 hours to fill the same tank. A, B and another pump C all together fill the tank in 2 hours. How long would pump C take, used alone, to fill the tank?
- A swimming pool can be filled by pipe A in 3 hours and by pipe B in 6 hours, each pump working on its own. At 9 am, pump A is started. At what time will the swimming pool be filled if pump B is started at 10 am?
- The sum of prime numbers that are greater than 60, but less than 70 is :