The cost of 3 books is Rs. 126. To find the cost of 8 books, we need to find the cost of 1 book first.
Cost of 1 book = 126 / 3 = 42
Cost of 8 books = 42 × 8 = 336
The line y = 3 is a horizontal line that intersects the y-axis at y = 3.
Since it's horizontal, it's parallel to the x-axis.
Given ratio: 5:7
To decrease 91 in the ratio 5:7, let's calculate the new value:
New value = 91 × 5/7
= 65
Let's find the new quantity:
Original quantity = 376
Ratio = 5:8
New quantity = (5/8) * 376
= 235
To find the maximum length of each piece, we need the HCF (Highest Common Factor) of 42, 54, and 64.
HCF of 42, 54, and 64 is 2 meters — the greatest length that divides all three without a remainder.
a:b = 8:9, b:c = 6:5
Make b same:
a:b = 16:18, b:c = 18:15
So, a:b:c = 16:18:15
Annual salary = Rs. 6000 × 12 = Rs. 72,000
Taxable income after rebate = Rs. 72,000 - Rs. 50,000 = Rs. 22,000
Income tax = 5% of Rs. 22,000 = Rs. 1100
This is an inverse proportion problem: More students → Less time.
20 × 8 = x × 5 → x = (20 × 8) / 5 = 32 students.
Let's analyze the sequence:
-5, 7, 19, 31
The differences between consecutive terms are:
7 - (-5) = 12
19 - 7 = 12
31 - 19 = 12
The sequence has a common difference of 12.
The general term for an arithmetic sequence is:
aₙ = a₁ + (n - 1)d
where a₁ is the first term (-5) and d is the common difference (12).
aₙ = -5 + (n - 1)12
aₙ = -5 + 12(n - 1)
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