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Question 1 of 5
1. Question
A refrigerator with marked price Rs. 32,000 is sold at successive discounts of 25% and 12%. The buyer spends Rs. 1,800 on transportation and then sells it for Rs. 29,000. What is the profit or loss percentage?
Correct
Answer: (c)
Explanation
Marked price = 32,000
Total discount = 25 + 12 – (25×12)/100
= 37 – 3 = 34%So the effective price = 66% of 32,000
= 0.66 × 32,000
= 21,120Add transportation cost = 1,800
Total CP = 21,120 + 1,800 = 22,920Selling price = 29,000
Profit = 29,000 – 22,920 = 6,080
Profit% = (6,080 ÷ 22,920) × 100
= 26.53%Incorrect
Answer: (c)
Explanation
Marked price = 32,000
Total discount = 25 + 12 – (25×12)/100
= 37 – 3 = 34%So the effective price = 66% of 32,000
= 0.66 × 32,000
= 21,120Add transportation cost = 1,800
Total CP = 21,120 + 1,800 = 22,920Selling price = 29,000
Profit = 29,000 – 22,920 = 6,080
Profit% = (6,080 ÷ 22,920) × 100
= 26.53% -
Question 2 of 5
2. Question
Akarsh invests Rs. x in corporate bonds which give him returns at 69% annually (simple for 1 year), and Rs. y in a mutual fund that gives 12% returns compounded half yearly. If Akarsh gets the same returns from both the investments after 1 year, then what is the square root of the ratio x : y?
Correct
Answer: (a)
Explanation
Amount from corporate bonds after one year:
A1 = (100 + 69)% of x = 169% of xFor mutual fund, 12% compounded half-yearly means 6% each half year.
Using net% effect:
Net% = a + b + (ab/100)Here, a = b = 6%
Net% effect = 6 + 6 + (6 × 6)/100
= 12 + 0.36
= 12.36%So effective annual rate = 12.36%
Amount from mutual funds after one year:
A2 = (100 + 12.36)% of y = 112.36% of yGiven A1 = A2
169% of x = 112.36% of y
169x = 112.36y
x / y = 112.36 / 169
Write 112.36 as fraction: 112.36 = 11236 / 100
So,
x / y = (11236 / 100) ÷ 169
= 11236 / 16900Divide numerator and denominator by 4:
= 2809 / 4225Note:
2809 = 53² and 4225 = 65²So, x / y = 53² / 65²
Taking square root,
√(x / y) = 53 / 65Hence, the square root of the ratio x : y is 53 : 65.
Incorrect
Answer: (a)
Explanation
Amount from corporate bonds after one year:
A1 = (100 + 69)% of x = 169% of xFor mutual fund, 12% compounded half-yearly means 6% each half year.
Using net% effect:
Net% = a + b + (ab/100)Here, a = b = 6%
Net% effect = 6 + 6 + (6 × 6)/100
= 12 + 0.36
= 12.36%So effective annual rate = 12.36%
Amount from mutual funds after one year:
A2 = (100 + 12.36)% of y = 112.36% of yGiven A1 = A2
169% of x = 112.36% of y
169x = 112.36y
x / y = 112.36 / 169
Write 112.36 as fraction: 112.36 = 11236 / 100
So,
x / y = (11236 / 100) ÷ 169
= 11236 / 16900Divide numerator and denominator by 4:
= 2809 / 4225Note:
2809 = 53² and 4225 = 65²So, x / y = 53² / 65²
Taking square root,
√(x / y) = 53 / 65Hence, the square root of the ratio x : y is 53 : 65.
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Question 3 of 5
3. Question
A clock gains 3% of the week-time during the first week and then gains 2% of the week-time during the next one week. If the clock was set right at 12 noon on a Friday, what will be the time that the clock will show exactly 14 days from the time it was set right?
Correct
Answer: (b)
Again, a week has 168 hours. In the first week, the clock gains 3% of 168 hours = (3/100) × 168 = 5.04 hours. So after the first week it is 5.04 hours fast. In the second week, it gains another 2% of 168 hours = (2/100) × 168 = 3.36 hours. So the additional gain in the second week is 3.36 hours. Net gain over the two weeks = 5.04 + 3.36 = 8.40 hours. Thus, after 14 days, when the actual time is 12 noon, the clock is 8.40 hours fast. Now 0.40 hours = 0.40 × 60 = 24 minutes, so 8.40 hours = 8 hours 24 minutes. Therefore, the clock will show 8:24 p.m. instead of 12 noon.
Hence, option (b) is correct.
Incorrect
Answer: (b)
Again, a week has 168 hours. In the first week, the clock gains 3% of 168 hours = (3/100) × 168 = 5.04 hours. So after the first week it is 5.04 hours fast. In the second week, it gains another 2% of 168 hours = (2/100) × 168 = 3.36 hours. So the additional gain in the second week is 3.36 hours. Net gain over the two weeks = 5.04 + 3.36 = 8.40 hours. Thus, after 14 days, when the actual time is 12 noon, the clock is 8.40 hours fast. Now 0.40 hours = 0.40 × 60 = 24 minutes, so 8.40 hours = 8 hours 24 minutes. Therefore, the clock will show 8:24 p.m. instead of 12 noon.
Hence, option (b) is correct.
-
Question 4 of 5
4. Question
A, B, C, D and E play a game of cards. A says to B, “If you give me five cards, you will then have twice as many cards as E has, and if I give you seven cards, you will then have as many cards as D has.” A and B together have 6 more cards than what C and D together have. C has four cards more than what E has. If the total number of cards is 108, how many cards does B have?
Correct
Answer: (d)
As per the question:
B − 5 = 2E …(i)
B + 7 = D …(ii)
A + B = C + D + 6 …(iii)
C = E + 4 …(iv)
A + B + C + D + E = 108 …(v)From (i),
B = 2E + 5 …(vi)From (ii),
D = B + 7 …(vii)From (iv),
C = E + 4 …(viii)Using (iii),
A + B = C + D + 6
= (E + 4) + (B + 7) + 6
= B + E + 17∴ A = E + 17 …(ix)
Now use (vi), (vii), (viii), (ix) in (v):
A + B + C + D + E
= (E + 17) + (2E + 5) + (E + 4) + (2E + 12) + E
= (E + 2E + E + 2E + E) + (17 + 5 + 4 + 12)
= 7E + 38 = 108∴ 7E = 70 ⇒ E = 10
From (vi),
B = 2E + 5 = 20 + 5 = 25Hence, option (d) is correct.
Incorrect
Answer: (d)
As per the question:
B − 5 = 2E …(i)
B + 7 = D …(ii)
A + B = C + D + 6 …(iii)
C = E + 4 …(iv)
A + B + C + D + E = 108 …(v)From (i),
B = 2E + 5 …(vi)From (ii),
D = B + 7 …(vii)From (iv),
C = E + 4 …(viii)Using (iii),
A + B = C + D + 6
= (E + 4) + (B + 7) + 6
= B + E + 17∴ A = E + 17 …(ix)
Now use (vi), (vii), (viii), (ix) in (v):
A + B + C + D + E
= (E + 17) + (2E + 5) + (E + 4) + (2E + 12) + E
= (E + 2E + E + 2E + E) + (17 + 5 + 4 + 12)
= 7E + 38 = 108∴ 7E = 70 ⇒ E = 10
From (vi),
B = 2E + 5 = 20 + 5 = 25Hence, option (d) is correct.
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Question 5 of 5
5. Question
A TV has a marked price of ₹25,000. It is sold at successive discounts of 20% and 5%. If the buyer spends ₹500 on transport and sells it at ₹21,500, find the profit or loss percentage.
Correct
Answer: (c)
Explanation:
Marked price = ₹25,000.
Total discount = 20 + 5 – (20×5)/100 = 25 – 1 = 24%.
Price after discount = 76% of 25,000 = ₹19,000.
Add transport = 19,000 + 500 = ₹19,500.
Selling price = ₹21,500.
Profit = 21,500 – 19,500 = ₹2,000.
Profit% = (2,000 / 19,500) × 100 = 10.26%Incorrect
Answer: (c)
Explanation:
Marked price = ₹25,000.
Total discount = 20 + 5 – (20×5)/100 = 25 – 1 = 24%.
Price after discount = 76% of 25,000 = ₹19,000.
Add transport = 19,000 + 500 = ₹19,500.
Selling price = ₹21,500.
Profit = 21,500 – 19,500 = ₹2,000.
Profit% = (2,000 / 19,500) × 100 = 10.26%
