# Ratio and Proportion level - 2 and level - 3 questions

Ratio and proportion topic throws us some really beautiful and hard questions.  Let us discuss a few questions.

Question 1:
If 30 men working 7 hours a day can make 12 tables in 18 days, how many days will 45 women working 9 hours a day take to make 32 chairs? Given, 4 men can make 3 tables in the same time as 3 women can make 4 chairs.
a. 12 days
b. 14 days
c. 28 days
d. 21 days
Explanation:
We cannot directly apply chain rule here as work is different in both cases as well as on the first job men are working and on the second women are working.

# Reasons behind rupee Demonetisation

What is the purpose of rupee demonetisation?  Does it reduce corruption?
I think the main motives behind the above said action are as follow:

A. Curbing the finances for terrorist activities temporarily:
One of the funding for terrorist organisations is printing fake currency.  There is approximately Rs.400 crore worth of fake curreny circulating in India and Rs.70 crore worth of fake currency pumped each year. (Source: The Hindu).  By demonetisation, the new money which is being pumped into the India will be stopped temporarily.  The money which is in stock with those terrorist organizations also rendered useless with this move.  But the fake money which is already in circulation only be removed by demonetisation.  So those terrorist organisations take some time to redesign their machines to print new fake money.  Because the recent Rs.500 fake notes are so perfect that common man may not find any difference.  So they already have the technology to re-create the security features. Therefore, we cannot say this step stops terrorism completely.

# Sum of the series by the method of differences

Let T1, T2, T3 ... are the terms of a series.
Then T2 - T1, T3 - T2, T4 - T3 . . . are called the series of the first order of differences. We denote it by 1d1, 1d2, 1d3. . .
Now, 1d2 - 1d1, 1d3 - 1d2, 1d3 - 1d2, . . . is called the series of the second order of differences. This is denoted as 2d1, 2d2, 2d3. . .
Now, 2d2 - 2d1, 2d3 - 2d2, 2d3 - 2d2, . . . is called the series of the third order of differences. This is denoted as 3d1, 3d2, 3d3. . .
General term of the above series =  ${T_n}$ = ${T_1}$ + $\left( {n - 1} \right) \times \left( {1{d_1}} \right)$ + $\dfrac{{(n - 1)(n - 2)}}{{1.2}} \times \left( {2{d_1}} \right)$ + . . .
(or)
${T_n} = {T_1}$ + ${}^{(n - 1)}{C_1} \times \left( {1{d_1}} \right)$ + ${}^{(n - 2)}{C_2} \times \left( {2{d_1}} \right)$ + . . .