BARC Quiz 5: Solution and Q&A

Quiz 5 - Part 1

1. Fred is more popular than Pete. Together they have 66 friends but Fred has 6 fewer than the square of the number that Pete has. How many friends does Fred have?
2. After 4/5 of his mangoes spoiled, Albert bought enough from Bryan so that each then had 1/3 as many as first and Albert had 80 more than Bryan. How many had Albert at first?
3. John ordered 4 pairs of black socks and some additional pairs of blue socks. The price of the black socks per pair was twice that of the blue. When the order was filled, it was found that the number of pairs of the two colors had been interchanged. This increased the bill by 50%. The ratio of the number of pairs of black socks to the number of pairs of blue socks in the original order was:

Quiz 5 - Part 2

1. Allan and Bernard start at the same time from two places 136 km apart and travel toward each other. Allan travels 10 kph and Bernard 8 kph. If Bernard rests 1 hour on the way, in how many hours will they meet?
2. In what time would Alberto, Brando and Carlo together do a work if Alberto alone could do it in 6 hours more, Brando alone in 1 hour more, and Carlo alone in twice the time?
3. Albert and Bryan can do a certain task if both work together 3 days and Albert then works alone 1 day. Bryan and Carl can do it if Bryan works 3 days and Carl works 10 days. It would take Carl 9 days longer than it would take Albert to do it alone. How long would Albert take if working alone?

Quiz 5 - Part 3

1. Amy can walk 4 km in the time it takes Baron to walk 5 km. Amy requires 3 minutes longer than Baron to walk a kilometer. Find the rate of Amy.
2. Andrea and Bethel run around a circular track whose circumference is 150m. When they run in opposite directions, they meet every 5 seconds, but when they run in the same direction from the same point, they are together every 25 seconds. Calculate the rate of Andrea.
3. Two candles of the same height are lighted at the same time. The first is consumed in 4 hours and the second in 3 hours. Assuming that each candle burns at a constant rate, in how many hours after being lighted was the first candle twice the height of the second?
4. At an ordinary rate a man can row the distance from Pasig to Manila, about 15km, in 5 hours less time than it takes him to return. Could he double his rate, his time to Manila would only be one hour less than his time to Pasig. What is the rate of Pasig River?