Question

Case Study based question -1
Labour suffer from Literacy
India’s literacy rate has increaed six times the end of the British rule in 1947, From 12% to 74% in recent times. Yet India has the world’s largest population of illiterate people acording to report of oxfam.

Ram asks the labour to dig a well up to a depth of 10m. Labour charges Rs.150 for first metre and Rs. 50 for each subsequent maters. As labour was uneducated, he claims Rs. 550 for the whole work.

(a) What type of series is formed from the given statement?
(i) A.P (ii) None A.P (iii) do not say anything (iv) None of the above.

(b) What should be the actual amount to be paid to the labour?
(i) Rs. 655 (ii) Rs. 600 (iii) Rs.645 (iv) Rs. 640

(c) How much money did ram will save, If he agree with Rs.550?
(i) Rs. 50 (ii) Rs. 40 (iii) Rs.45 (iv) Rs. 55

(d) If the first term of an A.P is a and nth term is b, then its common difference is
(I) $\frac{b-a}{n+1}$+1
(ii) $\frac{b-a}{n-1}$
(iii) $\frac{b-a}{n}$
(iv) $\frac{b+a}{n-1}$

(e) If A.P sequence has n terms then the third term from the last is given by
(i) l -2d (ii) l -d (iii) l -3d (iv) l -4d

Answer 1

Answer:

a) none of the above

b) Rs 600

c)

Answer 2

(a) The series formed is None A.P (option ii).

(b) The actual amount to be paid to labour is Rs.600 (option ii).

(c) Ram will save Rs.50 (option i).

(d) The common difference is $\frac{b-a}{n-1}$ (option ii).

(e) The third term from the last is given by l -2d (option i).

Given,

Ram asks the labour to dig a well up to a depth of 10m.

Labour charges Rs.150 for first metre and Rs. 50 for each subsequent meters.

As labour was uneducated, he claims Rs. 550 for the whole work.

To Find,

Answer of the given questions.

Solution,

Ram asks the labour to dig a well up to a depth of 10m.

Labour charges Rs.150 for first metre and Rs. 50 for each subsequent meters.

So, total amount should be paid = 150+(9×50) = 150+450= Rs.600

(a) The series that formed will be 150+50+50+50+50+50........... so on

It is not satisfying the conditions of an A.P.

So, it is None A.P.

(b) The actual amount that should be paid to labour  = 150+(9×50) = 150+450= Rs.600

(c) If he agrees with Rs.550 then, Ram will save

= 600 - 550 = Rs.50.

(d) first term = a , nth term = b and d =?

nth term = a+(n-1)d

(n-1)d = nth term - a

(n-1)d = b-a

d = $\frac{b-a}{n-1}$.

(e) If last term = l and common difference = d

third term from the last will be l-2d.

(a) The series formed is None A.P (option ii).

(b) The actual amount to be paid to labour is Rs.600 (option ii).

(c) Ram will save Rs.50 (option i).

(d) The common difference is $\frac{b-a}{n-1}$ (option ii).

(e) The third term from the last is given by l -2d (option i).

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