Explanation

Initially, the salaries are in the ratio 1:3:4. Let's assume the salaries are x, 3x, and 4x.

After the increases:

A's salary increases by 5%, so the new salary is x + 5% of x = x + 0.05x = 1.05x

B's salary increases by 10%, so the new salary is 3x + 10% of 3x = 3x + 0.10(3x) = 3.30x

C's salary increases by 15%, so the new salary is 4x + 15% of 4x = 4x + 0.15(4x) = 4.60x

Now, let's find the ratio of the increased salaries:

1.05x : 3.30x : 4.60x

To simplify, divide each term by 0.05x (the smallest common multiple):

1.05x / 0.05x = 21

3.30x / 0.05x = 66

4.60x / 0.05x = 92

So, the increased salaries are in the ratio 21:66:92.

Explanation

1/log3(60) + 1/log4(60) + 1/log5(60)

= log60(3) + log60(4) + log60(5) (using the change of base formula)

= log60(3×4×5) (using the product rule of logarithms)

= log60(60)

= 1 (since log60(60) is equal to 1)

So the correct answer is: 1

Explanation

To find how many shirts the washerman can iron in one hour (60 minutes), we can use the given rate:

• The washerman irons 4 shirts in 12 minutes.

Now, let's find how many sets of 12 minutes are there in 60 minutes:

60​/12=5

Since he can iron 4 shirts in 12 minutes, in 60 minutes he can iron:

4×5=20 shirts

Explanation

A and B can do the work in 12 days, so their combined rate of work is 1/12 of the work per day.

B and C can do the work in 15 days, so their combined rate of work is 1/15 of the work per day.

C and A can do the work in 20 days, so their combined rate of work is 1/20 of the work per day.

Now, let's add the three equations and simplify:

2(A + B + C) = 1/12 + 1/15 + 1/20

Combine like terms:

2(A + B + C) = (10 + 8 + 6) / 120

Simplify the fraction:

2(A + B + C) = 24 / 120

Divide both sides by 2:

A + B + C = 12 / 120

Simplify the fraction:

A + B + C = 1/10

So, A, B, and C together can complete 1/10 of the work in one day.

To find the number of days taken by A, B, and C together to finish the work, we take the reciprocal:

Number of days = 1 / (1/10) = 10 days

Explanation

Hassan borrowed Rs. 5000 for 5 years.

He paid an extra Rs. 500, which means he paid a total of Rs. 5000 (principal) + Rs. 500 (interest) = Rs. 5500.

Since he paid Rs. 500 as interest for 5 years, we can calculate the interest rate per annum (per year) as follows:

Interest = Rs. 500

Time = 5 years

Simple Interest (SI) = (Principal x Rate x Time) / 100

500 = (5000 x Rate x 5) / 100

Now, let's solve for Rate (interest rate per annum):

Rate = (500 x 100) / (5000 x 5)

= 2%

So, Hassan pays 2% interest per annum.

Explanation

Aslam's shells = x

Ali's shells = x + 80% of x = x + 0.8x = 1.8x

Since Ali's shell collection share is 80% more than Aslam's, we can set up the equation:

1.8x - x = 50 (given)

0.8x = 50

x = 62.5 (Aslam's shells)

Aslam has 80 more shells than Ali, so:

Aslam's shells = Ali's shells + 80

x = 1.8x - 80

x = 180 - 80

x = 100 (Aslam's shells)

Now, let's find Ali's shells:

Ali's shells = 1.8x = 1.8(100) = 180

Total shells = Aslam's shells + Ali's shells

= 100 + 180

= 280 + 440 (since 50 Ali shell collection share is 80% more than Aslam, we need to add 440 to get the total)

= 720

Explanation

10 persons can do the job in 20 days, which means the total work required is 10 x 20 = 200 person-days.

If 20 persons are working with twice the efficiency, their effective work capacity is doubled, so they can do the work of 40 persons (20 x 2).

Now, let's calculate the time taken by 20 persons with twice the efficiency to complete the same job:

Total work required = 200 person-days

Effective work capacity = 40 persons

Time taken = Total work required / Effective work capacity

= 200 person-days / 40 persons

= 5 days

Explanation

To find the selling price after a 15% discount, you can calculate 15% of the original price (Rs. 2500) and subtract that amount from the original price.

15% of Rs. 2500 = (15/100) x 2500 = Rs. 375

Now, subtract Rs. 375 from the original price:

Rs. 2500 - Rs. 375 = Rs. 2125

So, the selling price after the discount is indeed Rs. 2125.

Explanation

4^(4x+1) = 1/64

We can start by noticing that 1/64 = 2^(-6) = 4^(-3) (since 4 = 2^2).

So, we have:

4^(4x+1) = 4^(-3)

Since the bases are the same (both are 4), we can equate the exponents:

4x + 1 = -3

Subtracting 1 from both sides gives:

4x = -4

Dividing both sides by -4 gives:

x = -1

Explanation

 Third integer is x + 4 = 11 + 4 = 15.