Ratio and proportion questions: Tom and Harry's monthly salary ratio is 4: 3. Both save about 800 rupees a month. Their expense ratio is 3: 2, what is Tom's monthly income?

Question

Tom and Harry's monthly salary ratio is 4: 3. Both save about 800 rupees a month. Their expense ratio is 3: 2, what is Tom's monthly income?

Answer 1

Let's take this step by step. First, the 4:3 ratio means that for every 4 rupees Tom earns, Harry earns 3. Likewise, the 3:2 ratio means that for every 3 rupees Tom spends, Harry spends 2. Every rupee not spent is saved, and they both save 800, so that means that:

Tom salary - Tom expense = 800 = Harry salary - Harry expense

#1 Ts - Tx = 800 = Hs - Hx

#2 Ts - Tx = Hs - Hx

Now we know from the ratios that (4/3)Hs = Ts (for instance, if Hs were equal to 3, then (4/3)*3 = Ts = 4, which is what the ratio above says. This is because 4/3 = Ts/Hs, which is what the ratio is really telling us, we can only use this shortcut because we were working with the second number in the ratio.)

#3 Therefore, (from #1) (4/3)Hs - Tx = 800

#4 Likewise, we can see that (3/2)Hx = Tx, so (from #3) (4/3)Hs - (3/2)Hx = 800

#5 Since Hs - Hx also equals 800 (from #1), this means that (4/3)Hs - (3/2)Hx = Hs - Hx

Solving for Hs, we get (1/3)Hs - (1/2)Hx = 0

(1/3)Hs = (1/2)Hx

#6 Hs = (3/2)Hx

So Harry earns three halves (or 1.5 times) as much as he spends. Therefore:

(from #1 and #6) (3/2)Hx - Hx = 800

(1/2)Hx = 800

#7 Hx = 1,600 rupees

So Harry spends 1,600 rupees a month. Since he saved 800, he must earn 1,600 + 800, or 2,400.

#8 (from #1 and #7) Hs = 2,400

We know that the salary ratio is 4:3, meaning:

#9 (from definition of ratio and #8) 4/3 = Ts/2,400

Solving for this:

9,600/3 = Ts

#10 (from #9) Ts = 3,200

Therefore, the answer is 3,200 rupees. Incidentally, assuming this refers to Indian Rupees, that's about $46.68 here in America.