Question

The ratio of Henry's total points to that of Vincent's in a mock test was 6:7. In the next mock test, Henry's points increased by 70%. By what percentage must Vincent's points be increased if their total points were to be the same? Round off the answer(s) to the nearest whole number

Answer 1

Henry's score --- 6x
Vincent's score --- 7x

new score for Henry = 1.7(6x) = 10.2x
new score for Vincents = 7x(y/100)

7xy/100 = 10.2x
7y/100 = 10.2
7y = 1020
y = 145.71
So Vincent must increase his score by 45.7% or 46% to the nearest whole number.

check:
suppose Henry's score was 600 and Vincent score = 700
Henry's increased score = 1.7(600) = 1020
Vincent's increased score = 1.4571(700) = 1019.97 = appr 1020

my answer is correct

Answer 2

H/V = 6/7
H^1 = 1.7H
V^1 = H^1
V^1 = 1.7H
V^1 = 1.7 * 6V/7
V^1 = 1.457V
So, around 45.7% increase
or around 46%