Tag: math & puzzles

To solve this question, we need to determine the rate at which the painters work and then use that information to calculate the additional time required to complete the job when 24 more painters join the team.

Let's assume that the rate at which the 6 painters work is represented by the variable "R."

We know that the job can be completed by 6 painters in 28 days. So, the total work involved in the job is equal to 6 * 28 = 168 "painter-days."

Now, let's consider the scenario after 8 days when 24 more painters join the team. At this point, the work done by the 6 painters is equal to 6 * 8 = 48 "painter-days."

The remaining work to be done is equal to 168 - 48 = 120 "painter-days."

Since the number of painters has increased to 6 + 24 = 30, the rate at which the painters work can be represented by 30 * R.

Using the concept of "work done = rate * time," we can set up the equation:

120 = 30 * R * T,

where T is the additional time required to complete the job.

Simplifying the equation, we get:

120 = 30 * R * T, 4 = R * T.

Since we don't have any information about the rate at which the painters work, we can't determine the value of R. However, we can determine the value of T.

Therefore, the correct answer is D) 4.

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• Wrong explanation

To find out the number of gold coins the merchant has, we can solve the given problem using algebra.

Let's assume that the merchant has x gold coins. According to the problem, the merchant divides the coins into two unequal numbers.

Let's say the merchant divides the coins into two numbers, a and b, such that a > b.

According to the given information, we can form the following equation:

62(a - b) = a^2 - b^2

To solve this equation, let's simplify the equation using the difference of squares identity, (a^2 - b^2) = (a + b)(a - b):

62(a - b) = (a + b)(a - b)

Now, we can cancel out (a - b) from both sides:

62 = a + b

Since we know that a > b, we can deduce that a + b is the total number of gold coins the merchant has. Therefore, a + b = x.

Now, let's consider the answer options and substitute them into the equation a + b = x:

A) 82: 82 is not divisible by 62, so this option can be eliminated. B) 62: If we substitute a = 62 and b = 0 into the equation, we get 62 + 0 = 62, which satisfies the condition. This option is a potential answer. C) 42: 42 is not divisible by 62, so this option can be eliminated. D) 22: 22 is not divisible by 62, so this option can be eliminated.

Thus, the correct answer is B) 62.

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• Wrong explanation