Rohan and Sohan had certain amounts of money
with them. The ratio of the amounts with them is
8 : 5. Each day Rohan spends a certain amount and
Sohan earns one – sixth of the amount that Rohan
spends. After 9 days, the ratio of the amounts with
them is 10 : 11. After how many more days, will the
ratio of the amounts with them be 18 : 35?
Answers
Given : Rohan and Sohan had certain amounts of money with them . Each day Rohan spends a certain amount and Sohan earns one – sixth of the amount that Rohan spends After 9 days, the ratio of the amounts with
them is 10 : 11.
To find : fter how many more days, will the ratio of the amounts with them be 18 : 35
Solution:
The ratio of the amounts with Rohan and Sohan = 8 : 5
Roshan = 8M
Sohan = 5M
Let say Each day Rohan spends = 6S
Sohan Earns each day = 6S/6 = S
After 9 days Roshan has = 8M - 9*6S = 8M - 54S
After 9 Days Sohan has = 5M + 9S
(8M - 54S) / ( 5M + 9S ) = 10/11
=> 88M - 594S = 50M + 90S
=> 38M = 684S
=> M = 18S
Let say after D more days ratio of the amounts with them be 18 : 35
= (8M - 54S - 6DS) / (5M + 9S + DS) = 18/35
=> (144S - 54S - 6DS) / (90S + 9S + DS) = 18/35
=> (90S - 6DS)/(99S + DS) = 18/35
=> (90 - 6D )/(99 + D ) = 18/35
=> (15 - D )/(99 + D ) = 3/35
=> 525 - 35D = 297 + 3D
=> 38D = 228
=> D = 6
After 6 More days ratio of the amounts with them be 18 : 35
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Answer : d = 6
We can solve this problem by the following steps
Step 1) Let Rohan and Sohan had "x" and "y" amount of money respectively.
Step 2) Given that the ratio of amounts is 8:5
i.e. x:y = 8:5 or we can say x/y = 8/5. Therefore y = 5x/8.
Step 3) Suppose Rohan spends 6 Rs. and Sohan earns one-sixth of Rohan that is 1Rs. in a day.
For 9 days Rohan spends 9*6 = 54 Rs. and
For 9 days Sohan earns 9*1 = 9 Rs.
Step 4) Therefore ((x-9*6)/(y+9*1)) = 10/11.
Step 5) We get an equation that is 11x-594 = 10y+90 from step 4.
Step 6) Put the value of y from step 2 in the step 5 equation.
Step 7) From this we get the value of x = 144.
Step 8) Put the value of x in step 2 and we get the value of y = 90.
Step 9) Now we have to find how much day is needed to be in the ratio of 18:35. We form an equation that is (144 - 54 - 6d) / (90 + 9 + d) = 18/35
step10) (90 - 6d) / (99 + d) = 18/35
(90 - 6d )/(99 + d ) = 18/35
(15 - d )/(99 + d ) = 3/35
525 - 35d = 297 + 3d
38d = 228
d = 6