Question

if ram's income is 60 percent of shayam's income. if ram's expenditure is rupees 260 less than shaym's and their savings are 10% and 20% of their incomes, find their incomes respectively.

Answer 1

Answer:

Shyam's income is Rs 1000 and Ram's income is Rs 600

Step-by-step explanation:

Define x:

Let Shayam's income be x

Ram's income = 0.6x

Find the saving:

Ram's saving = 10% of 0.6x = 0.1 (0.6x) = 0.06x

Shayam's saving = 20% of x = 0.2x

Find their expenditure:

Ram's expenditure = 0.6x - 0.06x = 0.54x

Shayam's expenditure = x - 0.2x = 0.8x

Solve x:

Ram's expenditure is 260 less than Shayam's

0.8x - 0.54x = 260

0.26x = 260

x = 260 ÷ 0.26

x = 1000

Find their income:

Shayam = x = Rs 1000

Ram = 0.6x = 0.6(1000) = Rs 600

Answer: Shyam's income is Rs 1000 and Ram's income is Rs 600

Answer 2

Answer:

Ram's income is Rs 600, Shyam's income is Rs 1000

Step-by-step explanation:

Given if ram's income is 60 % of shayam's income and ram's expenditure is rupees 260 less than shaym's and their savings are 10% and 20% of their incomes, find their incomes respectively.

Let Shyam’s income be x. Therefore Ram’s income will be 60% of x which will be 0.6 x.

Let Shyam’s expenditure be y. Then Ram;s expenditure will be y – 260. We know expenditure is income – saving. Ram's saving is 10% and Shyam’s saving is 20%.

Thus if saving is 10% then expenditure will be 90%, and if saving is 20% then expenditure will be 80%.

So Ram’s income will be 0.9 x 0.6 x and Shyam’s will be 0.8 x

Now we have two equations  

  0.9 x 0.6 x = y – 260

      Y = 0.8 x

Solving this simultaneous equation and subtracting the above equation we get

   0.26 x = 260 or x = 260 / 0.26

 x = Rs 1000 and 0.6 x = 0.6 x 1000 = Rs 600

So Shyam’s income is Rs 1000 and Ram’s income is Rs 600