Explanation

He spent 3/5 of his savings, which means he spent (3/5)x.

He was left with Rs. 2,000, which means his initial savings minus the amount he spent equals Rs. 2,000:

x - (3/5)x = 2,000

Simplifying the equation:

(2/5)x = 2,000

Multiplying both sides by 5/2:

x = 2,000 x 5/2

x = 5,000

So, the man's initial savings were Rs. 5,000.

The correct answer is: Rs. 5,000

Explanation

Let N of 1/12 = 3/48.

Then, N = 3/48 x 12 = 3/4

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

Explanation

To find the fourth proportional, we need to set up a proportion:

60 : 48 :: 30 : x

Where x is the fourth proportional.

We can rewrite this as: 60/48 = 30/x

Cross-multiplying, we get: 60x = 30 × 48

Simplifying, we get: 60x = 1440

Dividing both sides by 60, we get: x = 24

So, the fourth proportional is 24.

Explanation

If it takes 6 people 6 days to do a job, the total amount of work can be considered as 6 people × 6 days = 36 person-days.

For 2 people to do the same amount of work:

Number of days = 36 person-days / 2 people = 18

So, it would take 2 people 18 days to do the job.

Explanation

Let's break it down step by step:

1. 4 boys = 5 girls, so 1 boy = 1.25 girls (since 5/4 = 1.25)
2. 2 women = 3 boys, so 1 woman = 1.5 boys (since 3/2 = 1.5)
3. 1 woman = 1.5 boys = 1.5 x 1.25 girls = 1.875 girls (since 1 boy = 1.25 girls)
4. 6 men = 7 women, so 1 man = 1.167 women (since 7/6 = 1.167)
5. Since 1 woman = 1.875 girls, 1 man = 1.167 x 1.875 girls = 2.188 girls
6. If a girl earns Rs. 400 per week, a man earns Rs. 2.188 x 400 = Rs. 875.20 per week
7. Daily earnings of a man = Rs. 875.20 / 7 = Rs. 125.00

So, the correct answer is Rs. 125.00.

Explanation

To calculate the interest, you can use the formula:

Interest = Principal × Rate × Time

In this case:

Principal (P) = Rs. 500

Rate (R) = 11% per annum = 0.11

Time (T) = 4 years

Interest = 500 × 0.11 × 4 = Rs. 220

So, Mr. Ali has to pay back the principal amount of Rs. 500 plus the interest of Rs. 220, making a total of Rs. 720.

The correct answer is: Rs. 220

Explanation

Since the student is 13th from the right, there are 12 students to their right.

And since they are 8th from the left, there are 7 students to their left.

To find the total number of students, you can add the number of students to their left and right, plus 1 (the student themselves):

7 (to the left) + 12 (to the right) + 1 (the student) = 20

So, there are 20 students in total.

Explanation

3.4% can be written as a fraction by dividing by 100 (since percent means "per hundred"):

3.4 ÷ 100 = 34 ÷ 1000

So, 3.4% is equal to the fraction 34/1000.

Explanation

600 units are made in 9 days with 20 machines.

To find the number of units made per day, divide 600 by 9: 600 ÷ 9 = 66.67 units per day.

Since there are 20 machines, the number of units made per day per machine is: 66.67 ÷ 20 = 3.33 units per day per machine.

Now, if we have 18 machines and want to produce units for 12 days, the total units that can be made are: 3.33 units per day per machine × 18 machines × 12 days = 720 units.

So, with 18 machines, the soap factory can produce 720 units in 12 days.