A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 22.09, the number of members in the group is?

Since 8 men in 24 days can reap 80 hectares.
? 1 men in 24 days can reap 80 / 8 hectares.
? 1 men in 1 days can reap 80 / 8 x 24 hectares.
? 36 men in 1 days can reap 80 x 36 / 8 x 24 hectares.
? 36 men in 30 days can reap 80 x 36 x 30 / 8 x 24 hectares.
? 36 men in 30 days can reap 10 x 36 x 30 / 24 hectares.
? 36 men in 30 days can reap 10 x 3 x 30 / 2 hectares.
? 36 men in 30 days can reap 10 x 3 x 15 hectares.
? 36 men in 30 days can reap 450 hectares.

As we know that Quarter Kg = 250 Gram
According to question,
250 Gram of potato costs 60 paise.
? 1 Gram of potato costs 60 / 250 paise.
? 200 Gram of potato costs 60 x 200 / 250 paise.
? 200 Gram of potato costs 60 x 20 / 25 paise.
? 200 Gram of potato costs 60 x 4 / 5 paise.
? 200 Gram of potato costs 12 x 4 paise.
? 200 Gram of potato costs 48 paise.

According to given question,
Since an industrial loom weaves 0.128 meters of cloth in 1 seconds.
? an industrial loom weaves 1 meters of cloth in 1 / 0.128 seconds.
? an industrial loom weaves 25 meters of cloth in 1 x 25 / 0.128 seconds.
? an industrial loom weaves 25 meters of cloth in 25 / 0.128 seconds.
? an industrial loom weaves 25 meters of cloth in 195 seconds.

Let the marked price = ? N
The discount equivalent to successive discounts 20 % and 10 % = { r₁ + r₂ - (r₁ r₂)/100 } %
Where, r₁ = 20 and r₂ = 10
Then, 30 - 2 = 28 %
According to the question,
{(100 - 28)N}/100 - {(100 - 30)N}/100 = 72
? (72N - 70N)/100 = 72
? N = (72 x 100)/2 = ? 3600

Given that, one root of the equation
x² - bx + c = 0 is square of other root of this equation i.e., roots (?, ?²).
? Sum of roots = ? + ?² = -(-b)/1
? ? (? + 1) = b .......(i)
and product of roots= ?. ?² = c/1
? ?³ = c ? = c^1/3 ....(ii)
From Eqs. (i) and (ii).
c^1/3 (c^1/3 + 1) = b ....(iii)
On cubing both sides, we get
c(c^1/3 + 1)³ = b³
? c {c + 1 + 3c^1/3 (c^1/3 + 1)} = b³
? c {c + 1 = 3b} = b³ [from Eq. (iii)]
? b³ = 3bc + c² + c

∴  x = 2.

2x + 3y = 29 ...(i)
and y = x + 3 ...(ii)
Putting the value of y from Eq. (ii) to Eq. (i), we get
2x + 3y = 29
2x + 3(x + 3) = 29
2x + 3x + 9 = 29
? 5x = 20
? x = 4

Let the wages of 1 man, 1 woman and 1 boy are ? P, ? Q and ? R, respectively. According to the question,
3P + 2Q + 4R = 26 ....(i)
3P = 4Q ....(ii)
and 2Q = 3R ....(iii)

From Eqs. (i) and (ii), we get
4Q + 2Q + 4R = 26
? 6Q + 4R = 26.........................(iv)

From Eqs. (iii) and (iv), we get
9R + 4R = 26
? 13R = 26
? R = 2
From Eqs. (ii) and (iii), we get
Q = 3 and P = 4

? Wages of 4 men, 3 women and 2 boys
= (4 x 4) + (3 x 3) + (2 x 2)
= 16 + 9 + 4 = ? 29

[?3 + x + ?3 - x] / [?3 + x - ?3 - x] = 2

Let ?3 + x = a and ?3 - x = b
Then, (a + b) / (a - b) = 2/1
? a + b = 2a - 2b
? a = 3b

? ?3 + x = 3?3 - x

On squaring bothv sides, we get
(?3 + x)² = (3?3 - x)²
? 3 + x = 9(3 - x)
? 3 + x = 27 - 9x
? 10x = 24
? x = 12/5

Let us assume the numbers are a and b.
According to question,
sum of two numbers = 25
a + b = 25......................(1)
difference of two numbers = 13
a - b = 13........................(2)
add the Equation (1) and (2)
a + b+ a - b = 25 + 13
? 2a = 38
? a = 19
Put the value of a in equation in (1)
19 + b = 25
? b = 25 - 19
? b = 6
Product of the numbers = a x b
put the value of a and b,
? Product of the numbers = 19 x 6
? Product of the numbers = 114