Direction : Read the data given below carefully and answer the questions.…
2020
Direction : Read the data given below carefully and answer the questions.
There are two schools A & B in a town. Total number of girls in school B are 30 more than twice of total number of girls in school A. Total number of boys in school B are equal to total number of students (boys + girls) in school A.
If total students in school B is 180 less than twice of total students in school A, then find the difference between total students in school A and total girls in school B?
Answer: E. None of these — Concept: This is a linear-equations word problem. Translate each verbal relationship into an algebraic equation using variables for the unknown counts. When…
- A.
240
- B.
280
- C.
420
- D.
210
- E.
None of these
Attempted by 10 students.
Show answer & explanation
Correct answer: E
Concept: This is a linear-equations word problem. Translate each verbal relationship into an algebraic equation using variables for the unknown counts. When the quantity asked for (here, a difference) turns out to depend only on a combination of variables that the equations pin down, that difference is uniquely determined even if the individual counts are not.
Setting up the variables:
Let girls in A = g and boys in A = b, so total students in A = g + b.
Girls in B = 2g + 30 (“30 more than twice the girls in A”).
Boys in B = g + b (“equal to the total students in A”).
Form the equation from the last condition:
Total students in B = (2g + 30) + (g + b) = 3g + b + 30.
“Total B is 180 less than twice total A” gives: 3g + b + 30 = 2(g + b) − 180.
Expand and simplify: 3g + b + 30 = 2g + 2b − 180.
Collect terms: g − b + 210 = 0, so b − g = 210.
Compute the requested difference:
Difference = (total students in A) − (total girls in B) = (g + b) − (2g + 30).
= b − g − 30 = 210 − 30 = 180.
Since 180 does not appear among the listed numeric choices (240, 280, 420, 210), the correct response is “None of these.”
Cross-check: Pick any valid values satisfying b = g + 210, say g = 50, b = 260. Then total A = 310, girls in B = 2(50)+30 = 130, and 310 − 130 = 180. The result is independent of the chosen g, confirming the difference is fixed at 180.