Question

India’s literacy rate has increased six times since 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 according to a 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 metres. As labour was uneducated, he claims Rs.550 for the whole work. (i) What type of series is formed from the given statement? a) AP b) None AP c) Do not say any thing d) None of the above (ii) What should be the actual amount to be paid to the labour? a) Rs.655 b) Rs.600 c) Rs.645 d)Rs. 640 (iii) How much money did Ram will save, if he agree with Rs.550? a) Rs.50 b) Rs.40 c) Rs.45 d) Rs.55 (iv) In AP sequence if each term is multiplied by constant k, then the new sequence will be a) AP b) None AP c) Do not say any thing d) None of the above (v) If AP sequence has n terms then the third term from the last is given by (where l is the last term of a sequence) a) l−2d b) l−d c) l−3d d) l−4d

Answer 1

❖ STEP-BY-STEP SOLUTION ❖

Given, the labour charge for the first metre is Rs. 150 and Rs. 50 for each subsequent metres.

Here the depth of the well is 10 metres.

Therefore the actual total labour charge is

Rs. {150 + (9 × 50)} = Rs. {150 + 450} = Rs. 600

Answers for the first three questions:

(i) What type of series is formed from the given statement?

• Ans. If we write the series for labour charge, it will be Rs. (150 + 50 + 50 + 50 + 50 + 50 + 50 + 50 + 50 + 50) and this is clearly not an AP.
• So, option (b) not AP is correct.

(ii) What should be the actual amount to be paid to the labour?

• Ans. The actual amount should be Rs. 600, which we have calculated earlier.
• So, option (b) Rs. 600 is correct.

(iii) How much money will Ram save, if he agrees with Rs. 550?

• Ans. Actual amount is Rs. 600 and miscalculated amount is Rs. 550. So Ram will save Rs. (600 - 550) = Rs. 50
• So, option (a) Rs. 50 is correct.

Let us solve the last two problems now:

(iv) In AP sequence if each term is multiplied by constant k, then what will be the new sequence?

• Ans. When each term of an AP sequence is multiplied by any constant k, then also the terms of the sequence be in AP.
• So, option (a) AP is correct.

(v) If AP sequence has n terms, then what will be third term from the last? (Where l is the last term of the sequence)

• Ans. Let d be the common difference.
• Here, the last term is l. Then the second term from the last is (l - d) and the third term from the last is (l - 2d).
• So, option (a) l - 2d is correct.