Ratio of Radio production

r_walid wrote:A company produces two types of radio: basic and deluxe.
of the stereos produced, 2/3 are basc and the rest delux.
if it takes 7/5 as many hours to produce a deluxe as it does to produce a basic, then what is the ratio of the number of hours it took to produce deluxe radio over the total hours it took to produce all radios?

7/17
14/31
7/15
17/35
1/2

IMO A

picked total number of radios as 60 -> delux =20 and basic = 40.

hrs it takes to produce delux = time to produce one delux radio * number of delux radios = 7/5 * 20 = 28

total hrs = 28 + 1*40 = 68

delux hrs / total hrs = 28/68 = 7/17.

OA pls.

I agree -- it helps here to just pick arbitrary (small and relevant) numbers that work with the fractions given:

Total radios should equal a multiple of 3:

2 basic
1 deluxe

Hrs to produce deluxe is 7/5 hrs to produce basic, so:

Time for basic = 5 hrs
Time for deluxe = 7 hrs

Total time for basics = 2*5 = 10 hrs
Total time for deluxes = 1*7 = 7 hrs

Deluxe / Total time = 7/(10+7) = 7/17