Concepts · Ranking and ordering
Counted from the left and from the right, the same person is counted twice.
Kabir has a ranking question in a mock test:
Meera is 9th from the left and 14th from the right in a row. How many people are in the row?
9 + 14 = 23. One line of addition. He ticks 23 and turns the page.
On photo day the class teacher lines up the back row and sends Kabir for chairs: “One for everyone in your row.”
Kabir counts along the row from the left end: he is third. From the right end: fifth. “Eight,” he says, and carries eight chairs over.
One chair is left over. He counts the row again, one head at a time: seven. He was in both of his counts: the three from the left ended on him, and the five from the right ended on him too.
Position from the left + position from the right = total + 1. The person is in both counts, so adding the two positions counts them twice: take one away for the total.
The same line, turned round, moves a position from one end to the other: from the right = total + 1 − from the left.
23 is what plain addition gives, and it can sit among the options.
In a row of 30, Kavya is 12th from the left. From the right she is 30 + 1 − 12 = 19th. Check: 12 + 19 = 31 = 30 + 1.
How many stand between two people? Put both on the same end first. In a row of 25, Ravi is 7th from the left and Sunil is 9th from the right, so Sunil is 25 + 1 − 9 = 17th from the left. Take the smaller position from the larger, 17 − 7 = 10: ten steps from Ravi to Sunil, and the last step lands on Sunil himself, so 9 stand between them: the 8th to the 16th.
A both-ends question can be settled with one line, left + right = total + 1. One too many and one too few can both sit among the options, right next to the right answer; the line, written down, picks between them.
1. Arun is 15th from the left and 11th from the right in a row. How many people are in the row?
Arun is in both counts.
25
15 + 11 = 26 counts Arun twice.
Take him out once: 26 − 1 = 25.
2. In a row of 40, Sana is 13th from the left. What is her position from the right?
Left + right = total + 1.
28th
From the right = total + 1 − from the left = 40 + 1 − 13.
= 28th. Check: 13 + 28 = 41 = 40 + 1.
3. In a row of 30, Asha is 6th from the left and Bina is 10th from the right. How many people stand between them?
Count both from the same end first.
14
Bina from the left: 30 + 1 − 10 = 21st.
Between the 6th and the 21st: 21 − 6 − 1 = 14. (The 7th to the 20th.)
A week later, Riya tries him with one:
Tara is 11th from the left and 6th from the right. How many are in the row?
Kabir writes 11 + 6 − 1 before he writes anything else. 16.
Ranking and ordering is one of the app’s topics. Every question there is answered before its solution shows.
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