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

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

Explanation

Let the number be x.  

x - 0.4x = 30 → 0.6x = 30 → x = 30 ÷ 0.6 = 50  

Explanation

25% of Rs. 1600 = 0.25 × 1600 = Rs. 400  

5% of Rs. 400 = 0.05 × 400 = Rs. 20  

Explanation

15% of 40 = 0.15 × 40 = 6  

Let the number be x.  

6 = 0.25x + 2 → 6 - 2 = 0.25x → 4 = 0.25x → x = 16