Explanation

The result of the expression $4^3 - frac{4^2}{2^2}$ is 60. ​

Explanation

Paid= 3/5

Remaining = 1 – 3/5 = 2/5

Given conditions:

2/5 x Total amount = 400

⇒       Total amount = 1000

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

The sentence is an example of "inversion."

It places the auxiliary verb "do" before the subject "the managers" to emphasize the rarity of the managers' responses.

Explanation

The correct direct narration of the indirect statement "We wanted to be confirmed that we were late" is: "We said, 'We are late, aren't we?'".

 It accurately reflects the desire for confirmation and uses a question format.

Explanation

The correct passive voice of the sentence "Your blame counts for nothing" is: "Your blame is worth nothing when it is counted."

This maintains the meaning of the original sentence in a passive construction.

Explanation

The correct sentence is: "Health is preferable to wealth."

The phrase "preferable to" is the proper way to compare two things in terms of preference.