Question

The ratio of the number of apples to the number of oranges in a grocery counter of 672 fruit items is 5:7. When some fresh stock of apples and oranges arrived, the number of oranges increased by 8, and the ratio of apples to oranges changed to 3:4. Find the number of apples that got added to the counter.

a) 144 apples
b) 96 apples
c) 120 apples
d) 80 apples

Answer 1

c) 120 applesTo maintain this new ratio, the number of apples should have been 300. Consequently, 20 apples were added (300 - 280), and considering the original ratio, the total number of apples added is 120.

Explanation:

Initially, the ratio of apples to oranges in the grocery counter of 672 fruit items was 5:7. This means there were
`\( 5 * (672)/(12) = 280 \)`apples and
`\( 7 * (672)/(12) = 392 \)`oranges. When some fresh stock arrived and the number of oranges increased by 8, the ratio changed to 3:4. This means the total number of oranges became
`\( 392 + 8 = 400 \).` To maintain the new ratio of 3:4, the number of apples must be \
`( (3)/(4) * 400 = 300`\). The increase in apples is
`\( 300 - 280 = 20 \)`apples. Thus, the number of apples added to the counter is
`\( 20 * 6 = 120 \).`

In the initial scenario, the apples and oranges formed a ratio of 5:7, amounting to 280 apples and 392 oranges respectively. Upon the arrival of new stock and the subsequent increase of 8 oranges, the revised ratio became 3:4, leading to a total of 400 oranges. To maintain this new ratio, the number of apples should have been 300. Consequently, 20 apples were added (300 - 280), and considering the original ratio, the total number of apples added is 120.