Dear Reader,
Below are three word problems based on chain rule dealing with direct and indirect proportions.
Question 1
If the cost of 714 numbers of notebooks is Rs.6069 then the approximate cost of 18 dozens of such notebooks is:
a) Rs. 1674 b) Rs. 1994.25 c) Rs. 2014.50 d) Rs. 1836
Answer : d) Rs. 1836
Solution :
Cost of 714 notebooks = Rs.6069
We have to find the cost of 18 dozen notebooks i.e., cost of 18 x 12 notebooks.
Let X be the cost of 18 dozen notebooks.
X = 18 x 12 x 6069 / 714
X = 1836
Question 2
If 16 men can dig a trench 160 meters long in 24 days, then how many meters can 18 men dig in 60 days?
a) 450 b) 525 c) 475 d) 490
Answer : a) 450
Solution :
The task is to be completed in 16 days by working 7.5 hours a day.
If Number of days increased then they dig more long - directly proportional
160 / ? = 16 / 18 x 24 /60
? = 160 x 18 x 24 / 16 x 24
? = 450
Hence, 18 men will dig 450 meters long in 60 days.
Question 3
If 11 tailors stitch 11 orders in 11 days, then 1 tailor will stitch 1 order in how many days?
a) 1 b) 11 c) 22 d) 121
Answer : b) 11
Solution :
Number of order decreases then number of days to complete also decreases - direct proportion
11 / ? = (11 / 1) x (1 / 11) (Since number of tailors indirectly proportional to days, 11 / 1 is changed reciprocally as 1 / 11)
? = 11 x 1 x 11 / 11 x 1
? = 11
Hence, 1 tailor will stitch 1 order in 11 days.
Below are three word problems based on chain rule dealing with direct and indirect proportions.
Question 1
If the cost of 714 numbers of notebooks is Rs.6069 then the approximate cost of 18 dozens of such notebooks is:
a) Rs. 1674 b) Rs. 1994.25 c) Rs. 2014.50 d) Rs. 1836
Answer : d) Rs. 1836
Solution :
Cost of 714 notebooks = Rs.6069
We have to find the cost of 18 dozen notebooks i.e., cost of 18 x 12 notebooks.
Let X be the cost of 18 dozen notebooks.
Notebooks Cost 714 6069 18x12 XHere the number of notebooks has decreased, so cost will also decrease. Hence notebook is directly proportional to cost.
X = 18 x 12 x 6069 / 714
X = 1836
Question 2
If 16 men can dig a trench 160 meters long in 24 days, then how many meters can 18 men dig in 60 days?
a) 450 b) 525 c) 475 d) 490
Answer : a) 450
Solution :
The task is to be completed in 16 days by working 7.5 hours a day.
Men Length Days 16 160 24 18 ? 60Here More men can dig more long - directly proportional
If Number of days increased then they dig more long - directly proportional
160 / ? = 16 / 18 x 24 /60
? = 160 x 18 x 24 / 16 x 24
? = 450
Hence, 18 men will dig 450 meters long in 60 days.
Question 3
If 11 tailors stitch 11 orders in 11 days, then 1 tailor will stitch 1 order in how many days?
a) 1 b) 11 c) 22 d) 121
Answer : b) 11
Solution :
Tailors Orders Days 11 11 11 1 1 ?Here the number of tailors decreased, day taken to complete will increase - indirect proportion
Number of order decreases then number of days to complete also decreases - direct proportion
11 / ? = (11 / 1) x (1 / 11) (Since number of tailors indirectly proportional to days, 11 / 1 is changed reciprocally as 1 / 11)
? = 11 x 1 x 11 / 11 x 1
? = 11
Hence, 1 tailor will stitch 1 order in 11 days.
