Explanation

• Let the two numbers be x and y.
• Given: x + y = 2490 ... (Equation 1)
• Also, 6.5% of x = 8.5% of y
• To simplify, convert percentages to decimals: 0.065x = 0.085y
• Now, divide both sides by 0.065: x = (0.085/0.065)y
• x = (85/65)y
• x = (17/13)y ... (Equation 2)
• Now, substitute Equation 2 into Equation 1:
• (17/13)y + y = 2490
• Combine like terms: (30/13)y = 2490
• Multiply both sides by 13/30: y = 1079
• Now that we have found y, we can find x:
• x = 2490 - y (from Equation 1)
• x = 2490 - 1079
• x = 1411
• So, the correct answer is: 1411, 1079

Explanation

Let the total distance be x km.

The man covers half the distance at 6 km/hr, so the time taken to cover this half is:

Time = Distance / Speed = (x/2) / 6 = x/12

The man covers the remaining half at 3 km/hr, so the time taken to cover this half is:

Time = Distance / Speed = (x/2) / 3 = x/6

The total time taken to cover the entire distance is the sum of the times taken to cover each half:

Total Time = x/12 + x/6

To add these fractions, we need a common denominator, which is 12. So we can rewrite the fractions as:

Total Time = x/12 + 2x/12 = 3x/12 = x/4

Now, we can find the average speed:

Average Speed = Total Distance / Total Time = x / (x/4) = 4 km/hr

So, the correct answer is: 4 km/hr

Explanation

Let the present age of the baby be x.

After 20 years, the baby's age will be x + 20.

According to the problem, the baby's age after 20 years will be 5 times the present age, so we can set up the equation: x + 20 = 5x

Subtract x from both sides: 20 = 4x

Divide both sides by 4: 5 = x

So, the present age of the baby is 5 years.

Explanation

Given: p/q = 7

We can rewrite this as: p = 7q

Now, let's evaluate the expression: p+q/p-q

Substitute p = 7q: (7q+q)/(7q-q)

Combine like terms: (8q)/(6q)

Simplify: 8/6

Divide both numerator and denominator by 2: 4/3

So, the correct answer is: 4/3

Explanation

Total number of votes polled$=(1136+7636+11628)=20400$
$\therefore$  Required Percentage

$=(\frac{11628}{20400}\times 100)$%
$=57$%

OR

Total number of votes polled

= (1,136 + 7,636 + 11,628)

= 20,400

Calculate percentage

= (11,628 / 20,400×100)

= 57%

Explanation

• Avg of 6 numbers = 30
• Sum of 6 numbers = 6 x 30 = 180
• Avg of first 4 numbers = 25
• Sum of first 4 numbers = 4 x 25 = 100
• Avg of last 3 numbers = 35
• Sum of last 3 numbers = 3 x 35 = 105
• Now, let's find the 4th number:
• Sum of first 3 numbers = Sum of first 4 numbers - 4th number
• = 100 - 4th number
• Sum of first 3 numbers = Sum of all 6 numbers - Sum of last 3 numbers
• = 180 - 105
• = 75
• So, 75 = 100 - 4th number
• 4th number = 100 - 75
• = 25

Explanation

To factorize the expression y^2 + y - 6, we need to find two numbers whose product is -6 and whose sum is 1 (the coefficient of the middle term).

These numbers are 3 and -2, so we can write:

y^2 + y - 6 = (y + 3)(y - 2)

Explanation

The given number 0.393939 is a repeating decimal, which can be written as:

0.39 39 39 ...

This is a repeating decimal with a block of 39 repeating indefinitely. To convert this to a fraction, we can use the following steps:

Let x = 0.393939...

Multiply both sides by 100 to get: 100x = 39.3939...

Subtract the original equation from this new equation to get: 99x = 39

Divide both sides by 99 to get: x = 39/99

So, the correct answer is: 39/99

Explanation

The mean of 100 items is 30, so the total sum of all items is:

30 x 100 = 3000

However, two items were wrongly taken as 32 and 12 instead of 23 and 11, which means the correct total sum should be:

3000 - 32 - 12 + 23 + 11 = 2990

Since there are 100 items, the correct mean is:

2990 ÷ 100 = 29.9

So, the correct answer is: 29.9

Explanation

Let third number = x

First number = 120/100 x = 6x/5

Second number = 150/ 100x = 3x/2

Ratio of two numbers = 6x/5 : 3x/2 = 12x : 15x = 4:5