Directions [1-5] : Study the following table charts carefully and answer the questions given beside.
A shopkeeper sold four products i.e. A, B, C and D. The cost price of product B is Rs. 4000 which is marked up by 25%. The marked price of product A is Rs. 250 less than the marked price of product B. The average of cost prices of the 4 products are Rs. 3137.5. He earns a profit of Rs. 1020 on selling product D. The marked price of product D is Rs. 950 more than the marked price of product C.
Product |
Discount Offered By Shopkeeper |
A |
20% |
B |
12% |
C |
30% |
Product |
Profit Percentage |
A |
25% |
C |
10% |
D |
100/3% |
1. Find the discount percentage offered by the shopkeeper on product D.
A. 12%
B. 15%
C. 18%
D. 20%
Answer: Option B
Explanation:
Following the common explanation, we get
Reqd.%
[latex]\frac {4800-4080}{4800}[/latex][latex]\times[/latex]100=15%
Hence, option B is correct.
Common explanation :
For product B :
Cost price = Rs. 4000
Marked price = 1.25 × 4000 = Rs. 5000
Percentage discount offered = 12%
Selling price = 0.88 × 5000 = Rs. 4400
Profit % earned =
[latex]\frac {4400-4000}{4000}[/latex][latex]\times[/latex]100=10%
For product A :
Marked price = 5000 – 250 = Rs. 4750
Percentage discount offered = 20%
Selling price = 0.8 × 4750 = Rs. 3800
Profit percentage earned = 25%
Cost Price =[latex]\frac {3800}{1.25}[/latex]=Rs. 3040
Total cost price of four products = 3137.5 × 4 = Rs. 12550
For product D:
Amount of profit earned = Rs. 1020
Profit percentage earned =[latex]\frac {100}{3}[/latex]%
So [latex]\frac {100}{3}[/latex]%1020
So, 100% = 1020 × 3 = 3060
So, the cost price of product D = Rs. 3060
Selling price = 3060 + 1020 = Rs. 4080
For product C :
Cost price = 12550 – (3060 + 4000 + 3040) = Rs. 2450
Profit percentage = 10%
Selling price = 1.1 × 2450 = Rs. 2695
Discount percentage = 30%
Marked price =[latex]\frac {2695}{0.7}[/latex]=3850
Marked price of D = 3850 + 950 = 4800
2. Find the total profit earned by the shopkeeper on selling all the four products.
A. Rs. 2520
B. Rs. 2320
C. Rs. 2425
D. Rs. 2475
Answer: Option C
Explanation:
Following the common explanation, we get
Required total profit = 760 + 400 + 245 + 1020 = Rs. 2425
Hence, option C is correct.
Common explanation :
For product B :
Cost price = Rs. 4000
Marked price = 1.25 × 4000 = Rs. 5000
Percentage discount offered = 12%
Selling price = 0.88 × 5000 = Rs. 4400
Profit % earned = [latex]\frac {4400-4400}{4000}[/latex][latex]\times[/latex]100 = 10%
For product A :
Marked price = 5000 – 250 = Rs. 4750
Percentage discount offered = 20%
Selling price = 0.8 × 4750 = Rs. 3800
Profit percentage earned = 25%
Cost Price = [latex]\frac {3800}{1.25}[/latex]= Rs. 3040
Total cost price of four products = 3137.5 × 4 = Rs. 12550
For product D:
Amount of profit earned = Rs. 1020
Profit percentage earned = [latex]\frac {100}{3}[/latex]%
So,[latex]\frac {100}{3}[/latex]% = 1020
So, 100% = 1020 × 3 = 3060
So, the cost price of product D = Rs. 3060
Selling price = 3060 + 1020 = Rs. 4080
For product C :
Cost price = 12550 – (3060 + 4000 + 3040) = Rs. 2450
Profit percentage = 10%
Selling price = 1.1 × 2450 = Rs. 2695
Discount percentage = 30%
Marked price = [latex]\frac {2695}{0.7}[/latex]= 3850
Marked price of D = 3850 + 950 = 4800
3. Had he sold the product C at the loss of 10%, then at what price he would have sold the product C.
A. Rs. 2205
B. Rs. 1960
C. Rs. 2375
D. Rs. 2280
Answer: Option A
Explanation:
Following the common explanation, we get
Required selling price of product C = 2450 × 0.9 = Rs. 2205
Hence, option A is correct.
Common explanation :
For product B :
Cost price = Rs. 4000
Marked price = 1.25 × 4000 = Rs. 5000
Percentage discount offered = 12%
Selling price = 0.88 × 5000 = Rs. 4400
Profit % earned =[latex]\frac {4400-4000}{4000}[/latex][latex]\times[/latex]100 = 10%
For product A :
Marked price = 5000 – 250 = Rs. 4750
Percentage discount offered = 20%
Selling price = 0.8 × 4750 = Rs. 3800
Profit percentage earned = 25%
Cost Price =[latex]\frac {3800}{1.25}[/latex]= Rs. 3040
Total cost price of four products = 3137.5 × 4 = Rs. 12550
For product D:
Amount of profit earned = Rs. 1020
Profit percentage earned = [latex]\frac {100}{3}[/latex]%
So, [latex]\frac {100}{3}[/latex]%= 1020
So, 100% = 1020 × 3 = 3060
So, the cost price of product D = Rs. 3060
Selling price = 3060 + 1020 = Rs. 4080
For product C :
Cost price = 12550 – (3060 + 4000 + 3040) = Rs. 2450
Profit percentage = 10%
Selling price = 1.1 × 2450 = Rs. 2695
Discount percentage = 30%
Marked price = [latex]\frac {100}{3}[/latex] = 3850
Marked price of D = 3850 + 950 = 4800
4. The selling price of product E is 100/11% more than the selling price of product B. If it is sold after offering two successive discounts of 20% and 25%, then find the marked price of product E.
A. Rs. 8400
B. Rs. 7500
C. Rs. 7200
D. Rs. 8000
Answer: Option D
Explanation:
Following the common explanation, we get
The selling price of product E = 100 + [latex]\frac {100}{11}[/latex]% of 4400 = 4800
The overall discount percentage offered of product E
= 20 + 25 – [latex]\frac {20 \times 25}{100}[/latex] = 40%
Marked price of product E = [latex]\frac {4800}{0.6}[/latex] = 8000
Hence, option D is correct.
Common explanation :
For product B :
Cost price = Rs. 4000
Cost price = Rs. 4000 Marked price = 1.25 × 4000 = Rs. 5000
Cost price = Rs. 4000 Percentage discount offered = 12%
Cost price = Rs. 4000 Selling price = 0.88 × 5000 = Rs. 4400
Profit % earned = [latex]\frac {4400-4000}{4000}[/latex][latex]\times[/latex]100 = 10%
For product A :
Marked price = 5000 – 250 = Rs. 4750
Percentage discount offered = 20%
Selling price = 0.8 × 4750 = Rs. 3800
Profit percentage earned = 25%
Cost Price =[latex]\frac {3800}{1.25}[/latex]= Rs. 3040
Total cost price of four products = 3137.5 × 4 = Rs. 12550
For product D:
Amount of profit earned = Rs. 1020
Profit percentage earned = [latex]\frac {100}{3}[/latex]%
So,[latex]\frac {100}{3}[/latex]% = 1020
So, 100% = 1020 × 3 = 3060
So, the cost price of product D = Rs. 3060
Selling price = 3060 + 1020 = Rs. 4080
For product C :
Cost price = 12550 – (3060 + 4000 + 3040) = Rs. 2450
Profit percentage = 10%
Selling price = 1.1 × 2450 = Rs. 2695
Discount percentage = 30%
Marked price = [latex]\frac {2695}{0.7}[/latex]= 3850
Marked price of D = 3850 + 950 = 4800
5. Find the difference between the selling prices of product C and selling price of product D.
A. Rs. 1410
B. Rs. 1425
C. Rs. 1295
D. None of these
Answer: Option D
Explanation:
Following the common explanation, we get
Required difference = 4080 – 2695 = 1385
Hence, option D is correct.
6. A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
Answer: Option C
Explanation:
C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 120% of Re. 1 = Rs [latex]\frac {6}{5}[/latex]
For Rs.[latex]\frac {6}{5}[/latex], toffees sold = 6
For Re. 1, toffees sold =6 [latex]\times[/latex] [latex]\frac {5}{6}[/latex] = 5
7. In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
A. 30%
B. 70%
C. 100%
D. 250%
Answer: Option B
Explanation:
Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295.
Required percentage = [latex]\frac {295}{420}[/latex][latex]\times[/latex] 100% [latex]\frac {1475}{21}[/latex]% = 70%(approximately).
8. The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
Answer: Option D
Explanation:
Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.
S.P. of x articles = Rs. 20.
Profit = Rs. (20 - x).
[latex]\frac {20 - x}{x}[/latex][latex]\times[/latex]100 = 25
2000 - 100x = 25x
125x = 2000
x = 16.
9. A shopkeeper sells some articles at a profit of 25% on the original price. What is the exact amount of profit? To find the answer, which of the following information given in Statements I and II is/are necessary
I. The sale price of the article
II. Number of articles sold
A. Only I is necessary
B. Only II is necessary
C. Either I or II is necessary
D. Both I and II are necessary
Answer: Option D
Explanation:
Gain = 25% of C.P.
In order to find gain, we must know the sale price of each article and the number of articles sold.
The correct answer is D.
10. A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary?
I. A number of toys sold.
II. The cost price of each toy.
A. Only I is necessary
B. Only II is necessary
C. Both I and II are necessary
D. Either I or II ins necessary
Answer: Option D
Explanation:
S.P. = Rs. 250 each.
To find gain percent, we must know the C.P. of each.
The correct answer is (B).
11. An amount of money is to be divided between P, Q, and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.X, and the difference between Q and R’s share is Rs.3000. Find the total amount of money?
A. 11000
B. 12400
C. 13200
D. 14300
Answer: Option C
Explanation:
12a-7a = 3000
5a = 3000
a = 600
7a-4a = x
3a = x
x = 1800
22*600 = 13200
12. If a certain amount X is divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/3 of what C gets, which of the following is true
A. C’s Share = 1053 and X = 1666
B. A’s Share = 238 and X = 1638
C. B’s Share = 234 and X = 1666
D. C’s Share = 1053 and X = 1638
Answer: Option D
Explanation:
A= 2/3 B; B= 1/3C;
A:B = 2:3 ; B:C = 1:3;
A:B:C = 2:3:9
C = 9/14 * 1638 = 1053
13. A sum of Rs.4880 was divided among boys and girls in such a way that each boy gets Rs.44.50 and each girl gets Rs. 55.25. If the total number of girls and boys is 100, find the number of girls?
Answer: Option C
Explanation:
x+y=100 ————– (i)
44.50x + 55.25y = 4880 ————– (ii)
Solving (i) and (ii) Y = 40
14. Which one of the following is not a prime number?
Answer: Option D
Explanation:
91 is divisible by 7. So, it is not a prime number.
15. How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
Answer: Option A
Explanation:
132 = 4 x 3 x 11
So, if the number divisible by all the three numbers 4, 3 and 11, then the number is divisible by 132 also.
264 11,3,4 (/)
396 11,3,4 (/)
462 11,3 (X)
792 11,3,4 (/)
968 11,4 (X)
2178 11,3 (X)
5184 3,4 (X)
6336 11,3,4 (/)
Therefore the following numbers are divisible by 132: 264, 396, 792 and 6336.
Required number of number = 4.
16. Which of the following is a prime number?
Answer: Option D
Explanation:
Clearly, 97 is a prime number.
17. The simple interest on a sum of money will be Rs. 200 after 5 yr. In the next 5 yr, principal is tripled. What will be the total interest at the end of the 10th yr?
A. ₹ 650
B. ₹ 850
C. ₹ 800
D. Can't be determined
Answer: Option C
Explanation:
According to the question,
SI for first 5 yrs = ₹ 200
SI for next 5 yrs = ₹ 200 x 3 = ₹ 600
∴ Total SI for 10 yr = ₹(200 + 600*) = ₹800.
When the principal is trebled, then SI for 5 yr will also be treble and hence SI for next 5 yr will be ₹ (200 × 3) = ₹ 600
Hence, option C is correct.
18. What decimal of an hour is a second?
A. 0025
B. 0256
C. 00027
D. 000126
Answer: Option C
Explanation:
Required decimal =[latex]\frac {1}{60\times60 = }[/latex] [latex]\frac {1}{3600}[/latex] = 00027
19. The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ?
A. 71 years
B. 72 years
C. 74 years
D. 77 years
Answer: Option A
Explanation:
Required sum = (80 - 3 x 3) years = (80 - 9) years = 71 years.
20. Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A ?
A. Rs. 4, Rs. 23
B. Rs. 13, Rs. 17
C. Rs. 15, Rs. 14
D. Rs. 17, Rs. 13
Answer: Option B
Explanation:
Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A.
Then, 2x + 3y = 77 ...(i) and
3x + 2y = 73 ...(ii)
Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17.
Putting y = 17 in (i), we get: x = 13.
21. A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have ?
Answer: Option C
Explanation:
Clearly, we have :
B-3 = E ...(i)
B + 3 = D ...(ii)
A+B = D + E+10 ...(iii)
B = C + 2 ...(iv)
A+B + C + D + E= 133 ...(v)
From (i) and (ii), we have : 2 B = D + E ...(vi)
From (iii) and (vi), we have : A = B + 10 ...(vii)
Using (iv), (vi) and (vii) in (v), we get:
(B + 10) + B + (B - 2) + 2B = 133 5B = 125 B = 25.
22. Which one of the following is not a prime number?
Answer: Option D
Explanation:
91 is divisible by 7. So, it is not a prime number.
23. Which of the following is a prime number ?
Answer: Option D
Explanation:
Clearly, 97 is a prime number.
24. If the number 91876 * 2 is completely divisible by 8, then the smallest whole number in place of * will be:
Answer: Option D
Explanation:
Then number 6x2 must be divisible by 8.
x = 3, as 632 is divisible 8.
25. 2056 x 987 = ?
A. 1936372
B. 2029272
C. 1896172
D. 1926172
Answer: Option B
Explanation:
2056 x 987 = 2056 x (1000 - 13)
= 2056 x 1000 - 2056 x 13
= 2056000 - 26728
= 2029272.