Use the formula:
% decrease = (increase ÷ (100 + increase)) × 100
= (25 ÷ 125) × 100 = 20%
So, to keep the total expenditure the same, consumption must decrease by 20%.
Given:
A1 = 28 (first term)
d = -4 (common difference)
n = 7 (number of terms)
To find the nth term (an), use the formula:
an = a + (n-1)d
an = 28 + (7-1)(-4)
= 28 + 6(-4)
= 28 - 24
= 4
Original score = 72
Improvement = 15% of 72
= 0.15 × 72
= 10.8
New score = Original score + Improvement
= 72 + 10.8
= 82.8
Given A:B = 3:4 and B:C = 12:13.
First, make the ratios for B consistent:
A:B = 3:4 = 9:12 (multiplied by 3)
Now, B:C = 12:13
A:B:C = 9:12:13
A:C = 9:13
The mean of the first five natural numbers (1, 2, 3, 4, 5) is 3
Calculated by summing the numbers (1 + 2 + 3 + 4 + 5 = 15) and dividing by the count of numbers (5).
Ratio of boys to girls = 5:3
If 5 parts = 40 boys, then 1 part = 40 ÷ 5 = 8
Girls = 3 parts = 8 × 3 = 24 girls.
Original price = 500
New price = 400
Decrease = 500 - 400 = 100
Percentage decrease = 100/500 × 100 = 1/5 × 100 = 20%
Given a : b : c = 3 : 4 : 7.
Let's find (a + b + c) : c or any other single term. Here we find (a + b + c) : a
a + b + c = 3 + 4 + 7 = 14
(a + b + c) : a = 14 : 3
Profit = 20% of Rs. 180 = 20/100 × 180 = 36
Selling Price = Cost Price + Profit = 180 + 36 = Rs. 216
0.13 × P² = 13
Solve for P²:
P² = 13 / 0.13 = 100
Now take the square root:
P = √100 = 10