GATE рдкреНрд░рд╢реНрди рдФрд░ рдЙрддреНрддрд░ рдХрд╛ рдЕрднреНрдпрд╛рд╕ рдХрд░реЗрдВ
рдкреНрд░: Three taps P, Q and R can fill a tank in 12 hrs, 15 hrs and 20 hrs respectively. If P is open all the time and Q and R are open for one hour each alternately, starting with Q, then the tank will be full in how many hours ? 2754 05b5cc6c0e4d2b4197774dafb
5b5cc6c0e4d2b4197774dafb- 19 hrsfalse
- 27 hrstrue
- 313 hrsfalse
- 411 hrsfalse
- рдЙрддреНрддрд░ рджреЗрдЦреЗрдВ
- Workspace
- SingleChoice
рдЙрддреНрддрд░ : 2. "7 hrs"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: B) 7 hrs Explanation: Given, P can fill in 12 hrs Q can fill in 15 hrs R can fill in 20 hrs => Volume of tank = LCM of 12, 15, 20 = 60 lit => P alone can fill the tank in 60/12 = 5 hrs => Q alone can fill the tank in 60/15 = 4 hrs => R alone can fill the tank in 60/20 = 3 hrs Tank can be filled in the way that (P+Q) + (P+R) + (P+Q) + (P+R) + .... => Tank filled in 2 hrs = (5+4) + (5+3) = 9 + 8 = 17 lit => In 6 hrs = 17 x 6/2 = 51 lit => In 7th hr = 51 + (5+4) = 51 + 9 = 60 lit => So, total tank will be filled in 7 hrs.
рдкреНрд░: рдХреМрди рд╕рд╛ рддрддреНрд╡ рдореИрдЧреНрдиреАрд╢рд┐рдпрдо рдХреА рддрд░рд╣ рд╕рдмрд╕реЗ рдЕрдзрд┐рдХ рд╡реНрдпрд╡рд╣рд╛рд░ рдХрд░рддрд╛ рд╣реИ? 2753 05b5cc60ae4d2b4197774b568
5b5cc60ae4d2b4197774b568- 1рд╕рд┐рд▓рд┐рдХреЙрдиfalse
- 2рд╕реНрдЯреНрд░реЛрдВрдЯрд┐рдпрдоtrue
- 3рд╕рд▓реНрдлрд░false
- 4рдЯрд┐рдиfalse
- рдЙрддреНрддрд░ рджреЗрдЦреЗрдВ
- Workspace
- SingleChoice
рдЙрддреНрддрд░ : 2. "рд╕реНрдЯреНрд░реЛрдВрдЯрд┐рдпрдо"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: B) рд╕реНрдЯреНрд░реЛрдВрдЯрд┐рдпрдо рд╡реНрдпрд╛рдЦреНрдпрд╛: рд╣рдо рдЬрд╛рдирддреЗ рд╣реИрдВ рдХрд┐ рдЖрд╡рд░реНрдд рд╕рд╛рд░рдгреА рдХреЗ рдПрдХ рд╣реА рд╕рдореВрд╣ рдХреЗ рддрддреНрд╡реЛрдВ рдореЗрдВ рд╕рдорд╛рди рд╡рд┐рд╢реЗрд╖рддрд╛рдПрдВ рд╣реЛрддреА рд╣реИрдВред рдпрд╣рд╛рдБ рдореИрдЧреНрдиреАрд╢рд┐рдпрдо рдФрд░ рд╕реНрдЯреНрд░реЛрдВрдЯрд┐рдпрдо рдиреЗ рдХреБрдЫ рд╕рдорд╛рди рдЧреБрдг рд╕рд╛рдЭрд╛ рдХрд┐рдП рдХреНрдпреЛрдВрдХрд┐ рд╡реЗ рджреЛрдиреЛрдВ рдПрдХ рд╣реА рд╕рдореВрд╣ рдХреЗ рд╣реИрдВред Sr рд╕реНрдЯреНрд░реЛрдВрдЯрд┐рдпрдо рдХрд╛ рд░рд╛рд╕рд╛рдпрдирд┐рдХ рдкреНрд░рддреАрдХ рд╣реИ рдЬреЛ рдПрдХ рд╕рдореВрд╣ рджреЛ рддрддреНрд╡ рд╣реИ; рдЗрд╕рдХрд╛ рдкрд░рдорд╛рдгреБ рдХреНрд░рдорд╛рдВрдХ 38 рд╣реИред
рдкреНрд░: A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained ? 2751 05b5cc6dce4d2b4197774e960
5b5cc6dce4d2b4197774e960- 15:3false
- 21:4false
- 34:1false
- 49:1true
- рдЙрддреНрддрд░ рджреЗрдЦреЗрдВ
- Workspace
- SingleChoice
рдЙрддреНрддрд░ : 4. "9:1"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: D) 9:1 Explanation: Milk = 3/5 x 20 = 12 liters, water = 8 liters If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters. Remaining milk = 12 - 6 = 6 liters Remaining water = 8 - 4 = 4 liters 10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters. The ratio of milk and water in the new mixture = 16:4 = 4:1 If the process is repeated one more time and 10 liters of the mixture are removed, then amount of milk removed = 4/5 x 10 = 8 liters. Amount of water removed = 2 liters. Remaining milk = (16 - 8) = 8 liters. Remaining water = (4 -2) = 2 liters. Now 10 lts milk is added => total milk = 18 lts The required ratio of milk and water in the final mixture obtained = (8 + 10):2 = 18:2 = 9:1.
рдкреНрд░: The average age of a couple and their son was 40 years, the son got married and a child was born just two years after their marriage. When child turned to 10 years, then the average age of the family becomes 38 years. What was the age of the daughter in law at the time of marriage ? 2743 05b5cc6c6e4d2b4197774de59
5b5cc6c6e4d2b4197774de59- 112 yearstrue
- 210 yearsfalse
- 314 yearsfalse
- 413 yearsfalse
- рдЙрддреНрддрд░ рджреЗрдЦреЗрдВ
- Workspace
- SingleChoice
рдЙрддреНрддрд░ : 1. "12 years"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: A) 12 years Explanation: Given the average age of couple and their son = 40 => Sum of age (H +W +S) = 40├Ч3 Let the age of daughter in law at the time of marriage = D years Now after 10 years, (H + S +W) + 3├Ч12 + D +12 + 10 = 38├Ч5 178 + D = 190 D = 190 -178 = 12 years
рдкреНрд░: How many parallelograms will be formed if 7 parallel horizontal lines intersect 6 parallel vertical lines? 2739 05b5cc754e4d2b4197774fbb4
5b5cc754e4d2b4197774fbb4- 1215false
- 2315true
- 3415false
- 4115false
- рдЙрддреНрддрд░ рджреЗрдЦреЗрдВ
- Workspace
- SingleChoice
рдЙрддреНрддрд░ : 2. "315"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: B) 315 Explanation: Parallelograms are formed when any two pairs of parallel lines (where each pair is not parallel to the other pair) intersect. Hence, the given problem can be considered as selecting pairs of lines from the given 2 sets of parallel lines. Therefore, the total number of parallelograms formed = 7C2 x 6C2 = 315
рдкреНрд░: Three men, four women and six children can complete a work in 9 days. A women does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 9 days? 2738 05b5cc6b2e4d2b4197774d374
5b5cc6b2e4d2b4197774d374- 17true
- 28false
- 39false
- 46false
- рдЙрддреНрддрд░ рджреЗрдЦреЗрдВ
- Workspace
- SingleChoice
рдЙрддреНрддрд░ : 1. "7"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: A) 7 Explanation: Given (3 Men + 4 Women + 6 Children) -----> 9 days But W = 2M and C = M/2 Now, convert Men and Children into Women by 3W2 + 4W + 6W4=> 32 + 4 + 32 = 7 Women Therefore, 7 women alone can complete this work in 9 days.
рдкреНрд░: If (1 ├Ч 2 ├Ч 3 ├Ч 4 ........ ├Ч n) = n!, then 15! - 14! - 13! is equal to ___? 2737 05b5cc6bee4d2b4197774d997
5b5cc6bee4d2b4197774d997- 114 ├Ч 13 ├Ч 13!false
- 215 ├Ч 14 ├Ч 14!false
- 314 ├Ч 12 ├Ч 12!false
- 415 ├Ч 13 ├Ч 13!true
- рдЙрддреНрддрд░ рджреЗрдЦреЗрдВ
- Workspace
- SingleChoice
рдЙрддреНрддрд░ : 4. "15 ├Ч 13 ├Ч 13!"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: D) 15 ├Ч 13 ├Ч 13! Explanation: 15! - 14! - 13! = (15 ├Ч 14 ├Ч 13!) - (14 ├Ч 13!) - (13!) = 13! (15 ├Ч 14 - 14 - 1) = 13! (15 ├Ч 14 - 15) = 13! x 15 (14 - 1) = 15 ├Ч 13 ├Ч 13!
рдкреНрд░: If 15 men 4 hours per day works for 14 days get Rs.35/- then how many men required if the work is 8 hours per day for 10 days they get 50/- ? 2734 05b5cc754e4d2b4197774fb68
5b5cc754e4d2b4197774fb68- 112false
- 213false
- 314false
- 415true
- рдЙрддреНрддрд░ рджреЗрдЦреЗрдВ
- Workspace
- SingleChoice
рдЙрддреНрддрд░ : 4. "15"
рд╡реНрдпрд╛рдЦреНрдпрд╛ :
Answer: D) 15 Explanation: We know M1├ЧD1├ЧH1W1 = M2├ЧD2├ЧH2W2 => 15├Ч4├Ч1435 = M├Ч8├Ч1050 => M = 15