86. The present age of a father is 3 years more than three times the age of his son. Three years hence, father’s age will be 10 years more than twice the age of the son. Find the present age of the father.
(A) 30 years
(B) 40 years
(C) 33 years
(D) 35 years
Answer:
(C) 33 years
Explanation:
Let Son’s age = S and Father’s = F. F = 3S + 3. In 3 years: F + 3 = 2(S + 3) + 10. Substituting F gives: (3S + 3) + 3 = 2S + 16, which means 3S + 6 = 2S + 16, so S = 10. Father’s age F = 3(10) + 3 = 33.
87. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
(A) 4 days
(B) 5 days
(C) 6 days
(D) 7 days
Answer:
(A) 4 days
Explanation:
10(6M + 8B) = 2(26M + 48B). This simplifies to 60M + 80B = 52M + 96B, so 8M = 16B or 1M = 2B. Converting men to boys: 6M + 8B = 12B + 8B = 20B. 20 boys take 10 days. 15M + 20B = 30B + 20B = 50 boys. 50 boys will take (20 * 10) / 50 = 4 days.
88. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
(A) 3
(B) 5
(C) 7
(D) 9
Answer:
(C) 7
Explanation:
10 women complete the work in 7 days, so 5 women (half the workforce) will complete it in 14 days. This means 5 women do 1/14 of the work per day. 10 children do 1/14 of the work per day. Together, they do 1/14 + 1/14 = 2/14 = 1/7 of the work per day. Thus, they will take 7 days.
89. A thief is spotted by a policeman from a distance of 100 meters. When the policemen start the chase, the thief also starts running. If the speed of the thief be 8 kmph and that of the policemen 10 kmph, how far the thief will have run before he is overtaken?
(A) 400 m
(B) 500 m
(C) 800 m
(D) 850 m
Answer:
(A) 400 m
Explanation:
The relative speed is 10 – 8 = 2 km/h. Distance to cover is 100 m = 0.1 km. Time taken to catch the thief = 0.1 / 2 = 0.05 hours. In 0.05 hours, the thief runs 8 km/h * 0.05 h = 0.4 km = 400 meters.
90. A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
(A) 3.6
(B) 7.2
(C) 8.4
(D) 10
Answer:
(B) 7.2
Explanation:
5 minutes = 300 seconds. Speed = Distance / Time = 600 m / 300 s = 2 m/s. To convert m/s to km/h, multiply by 18/5: 2 * (18/5) = 36/5 = 7.2 km/h.
