Explanation

Set up the ratio.

By definition, if x is the mean proportional between two numbers a and b, they form a geometric progression:

a/x: x/b

Substituting a=2 and b=4

2/x: x/8

Explanation

Let total salary = S

1. Spends 1/3 on personal affairs → Remaining = (2/3)S  

2. Gives half of remaining to wife → Remaining after this = (1/2) × (2/3)S = (1/3)S  

3. Invests 75% of final remaining → Invested = 75% of (1/3)S = (3/4) × (1/3)S = (1/4)S  

   So final amount left after investing = Remaining - Invested = (1/3)S - (1/4)S = (4/12 - 3/12)S = (1/12)S

Given this final amount = 1000  

So, (1/12)S = 1000  

=> S = 1000 × 12 = 12,000

Explanation

Casey can carry 4 boxes per trip.

Total boxes = 33

Number of trips = 33 ÷ 4 = 8.25

Since he can’t make a fraction of a trip, he needs 9 trips.

Explanation

o find average speed:

Speed = Distance ÷ Time

Distance = 7 miles  

Time = 40 minutes = 40 ÷ 60 = 2/3 hours

Speed = 7 ÷ (2/3) = 7 × (3/2) = 10.5 mph

Explanation

Since the expression includes multiplication by zero (6 × 4 × 0 × 100 × 0.34), the entire product is zero.

Explanation

To find the average:

(25 + 20 + 17 + 19) ÷ 4  

= 81 ÷ 4  

= 20.25

Explanation

x = average of k and 15 = (k + 15) / 2  

y = average of k and 5 = (k + 5) / 2  

Average of x and y = (x + y) / 2  

= [ (k + 15)/2 + (k + 5)/2 ] / 2  

= [ (k + 15 + k + 5) / 2 ] / 2  

= (2k + 20) / 4  

= (k + 10) / 2  

Explanation

Work = Number of workers × Time

Let’s find the total work in worker-hours:

- 8 workers × 36 hours = 288 worker-hours

Now, to finish the work in 8 hours, let’s find how many total workers are needed:

- 288 ÷ 8 = 36 workers

We already have 8 workers, so additional workers needed:

- 36 − 8 = 28

Explanation

We are given a letter pair sequence: AD, DF, EH, ?

First letters:

- A → D (+3)

- D → E (+1)

- E → G (+2)

So the pattern in first letters is: +3, +1, +2

Second letters:

- D → F (+2)

- F → H (+2)

- H → J (+2)

So the pattern in the second letters is consistently +2

Therefore, the missing pair is:

GJ

Explanation

Let the first part be x, lent at 10% for 8 years.  

So, interest = (x × 10 × 8)/100 = 0.8x

Let the second part be (4200 − x), lent at 7% for 5 years.  

So, interest = [(4200 − x) × 7 × 5]/100 = (35/100)(4200 − x) = 0.35(4200 − x)

Since both interests are equal:

0.8x = 0.35(4200 − x)

Solve:

0.8x = 1470 − 0.35x  

0.8x + 0.35x = 1470  

1.15x = 1470  

x = 1278.26

So, second part = 4200 − 1278.26 = Rs. 2,921.74 ≈ Rs. 2,921