TEST - 8
1. The average of the ages of a man and his daughter is 34 years. If the respective ratio of their ages four years from now is 14: 5,what is daughter’s present age? (a) 10 years (b) 12 years (c) 18 years (d) none of these Explanation: Average age of man and his daughter = 34 years Their total age = (34 × 2) years = 68 years Let man’s age be x years, Then daughter age = (68 – x) years ∴x+468−x+4=145⇒5(x+4)=14(72−x)⇒5x+20=1008−14x⇒19x=988⇒x=52 ∴ Daughter’s present age = (68 – 52) years = = 16 years |
1. The average of the ages of a man and his daughter is 34 years. If the respective ratio of their ages four years from now is 14: 5,what is daughter’s present age? (a) 10 years (b) 12 years (c) 18 years (d) none of these Explanation: Average age of man and his daughter = 34 years Their total age = (34 × 2) years = 68 years Let man’s age be x years, Then daughter age = (68 – x) years ∴x+468−x+4=145⇒5(x+4)=14(72−x)⇒5x+20=1008−14x⇒19x=988⇒x=52 ∴ Daughter’s present age = (68 – 52) years = 16 years |
2. The age of a father 10 years ago was thrice the age of his son. 10 years hence, the father’s age will be twice that of his son. The ratio of their present age is = ? (a) 8 : 5 (b) 7 : 3 (c) 9 : 5 (d) 5 : 2 Explanation: Let son’s age 10 years ago be x years Then, father age 10 years ago = 3x years Son’s age now = (x + 10) years, Father age now = (3x+ 10) years (3x+10)+10=2[(x+10)+10]⇒3x+20=2(x+20)⇒3x+20=2x+40⇒x=20 Ratio of present ages of father and son = 3x+10x+10=3×20+1020+10=7030=73=7:3 |
2. The age of a father 10 years ago was thrice the age of his son. 10 years hence, the father’s age will be twice that of his son. The ratio of their present age is = ? (a) 8 : 5 (b) 7 : 3 (c) 9 : 5 (d) 5 : 2 Explanation: Let son’s age 10 years ago be x years Then, father age 10 years ago = 3x years Son’s age now = (x + 10) years, Father age now = (3x+ 10) years (3x+10)+10=2[(x+10)+10]⇒3x+20=2(x+20)⇒3x+20=2x+40⇒x=20 Ratio of present ages of father and son = 3x+10x+10=3×20+1020+10=7030=73=7:3 |
3. At present Subhan’s age is twice the age of his daughter. After 6 year from now, the ratio of the ages of Subhan and his daughter will be 23: 13. What is the present age of Subhan? (a) 36 years (b) 40 years (c) 46 years (d) none of these Explanation: Let daughter’s age be x years. Sobhan’s age = 2x years ∴2x+6x+6=2313⇒13(2x+6)=23(x+6)⇒26x+78=23x+138⇒3x=60⇒x=20 Present age of Subhan = 2x years = (2×20) years = 40 years |
3. At present Subhan’s age is twice the age of his daughter. After 6 year from now, the ratio of the ages of Subhan and his daughter will be 23: 13. What is the present age of Subhan? (a) 36 years (b) 40 years (c) 46 years (d) none of these Explanation: Let daughter’s age be x years. Sobhan’s age = 2x years ∴2x+6x+6=2313⇒13(2x+6)=23(x+6)⇒26x+78=23x+138⇒3x=60⇒x=20 Present age of Subhan = 2x years = (2×20) years = 40 years |
4. Ten years ago, a man was seven times as old as his son. Two years hence, twice his age will be equal to five times the age of his son. What is the present age of the son ? (a) 12 years (b) 13 years (c) 14 years (d) 15 years Explanation: Let son’s age 10 years ago be x years. Then, man’s age 10 years ago = 7x years Son’s present age = (x + 10) years, Man’s present age = (7x + 10) years ∴2[(7x+10)+2] = 5[(x+10)+2]⇒2(7x+12)=5(x+12)⇒14x+24=5x+60⇒9x=36⇒x=4 Son’s present age = (x + 10) years = (4 + 10) years = 14 years |
4. Ten years ago, a man was seven times as old as his son. Two years hence, twice his age will be equal to five times the age of his son. What is the present age of the son ? (a) 12 years (b) 13 years (c) 14 years (d) 15 years Explanation: Let son’s age 10 years ago be x years. Then, man’s age 10 years ago = 7x years Son’s present age = (x + 10) years, Man’s present age = (7x + 10) years ∴2[(7x+10)+2] = 5[(x+10)+2]⇒2(7x+12)=5(x+12)⇒14x+24=5x+60⇒9x=36⇒x=4 Son’s present age = (x + 10) years = (4 + 10) years = 14 years |
5. The ages of Samina and Sana are in the ratio of 7:3 respectively. After 6 years, the ratio of their ages will be 5:3. What is the difference in their ages? (a) 6 years (b) 8 years (c) 10 years (d)12 years Explanation: Let Samina’s age be 7x years. Then, Sana’s age = 3x years ∴7x+63x+6=53⇒3(7x+6)=5(3x+6)⇒21x+18=15x+30⇒6x+12⇒x=2 Difference in their ages = (7x – 3x) years = 4x years = (4 × 2) years = 8 years |
5. The ages of Samina and Sana are in the ratio of 7:3 respectively. After 6 years, the ratio of their ages will be 5:3. What is the difference in their ages? (a) 6 years (b) 8 years (c) 10 years (d)12 years Explanation: Let Samina’s age be 7x years. Then, Sana’s age = 3x years ∴7x+63x+6=53⇒3(7x+6)=5(3x+6)⇒21x+18=15x+30⇒6x+12⇒x=2 Difference in their ages = (7x – 3x) years = 4x years = (4 × 2) years = 8 years |
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6. The ages of A and B are presently in the ratio of 5: 6 respectively. Six years hence, this ratio became 6: 7 respectively. What was B’s age 5 years ago? (a) 25 years (b) 30 years (c) 31 years (d) 36 years Explanation: Let A’s age be 5x years. Then, B’s age = 6x years ∴5x+66x+6=67⇒7(5x+6)=6(6x+6)⇒35x+42=36x+36⇒x=6 B’s age 5 years ago = (6x – 5) years = (6 × 6 – 5) years = 31 years |
6. The ages of A and B are presently in the ratio of 5: 6 respectively. Six years hence, this ratio became 6: 7 respectively. What was B’s age 5 years ago? (a) 25 years (b) 30 years (c) 31 years (d) 36 years Explanation: Let A’s age be 5x years. Then, B’s age = 6x years ∴5x+66x+6=67⇒7(5x+6)=6(6x+6)⇒35x+42=36x+36⇒x=6 B’s age 5 years ago = (6x – 5) years = (6 × 6 – 5) years = 31 years |
7. The sum of the ages of a daughter and her mother is 56 years. After 4 years, the age of the mother will be three times that of the daughter. At present their ages are ? (a) 10 years , 46 years (b) 12 years , 44 years (c) 11 years , 45 years (d) 13 years , 43 years Explanation: Let daughter’s age be x years. Then, mother’s age = (56 −x) years (56−x)+4=3(x+4)⇒60−x=3x+12⇒4x=48⇒x=12 ∴ Daughter’s age = 12 years And the mother’s age = (56 −12) = 44 years |
7. The sum of the ages of a daughter and her mother is 56 years. After 4 years, the age of the mother will be three times that of the daughter. At present their ages are ? (a) 10 years , 46 years (b) 12 years , 44 years (c) 11 years , 45 years (d) 13 years , 43 years Explanation: Let daughter’s age be x years. Then, mother’s age = (56 −x) years (56−x)+4=3(x+4)⇒60−x=3x+12⇒4x=48⇒x=12 ∴ Daughter’s age = 12 years And the mother’s age = (56 −12) = 44 years |
8. The present age of son is half of the present age of his mother. Ten years ago, his mother’s age was thrice the age of her son. What is the present age of the son? (a) 20 years (b) 25 years (c) 30 years (d) 40 years Explanation: Let mother’s age be 2x years, Then, son’s age = x years ∴(2x−10)=3(x−10)⇒2x−10=3x−30⇒x=20 Son’s age = 20 years |
8. The present age of son is half of the present age of his mother. Ten years ago, his mother’s age was thrice the age of her son. What is the present age of the son? (a) 20 years (b) 25 years (c) 30 years (d) 40 years Explanation: Let mother’s age be 2x years, Then, son’s age = x years ∴(2x−10)=3(x−10)⇒2x−10=3x−30⇒x=20 Son’s age = 20 years |
9. Rohan’s son’s age is 1/3 of Rohan’s wife’s age. Rohan’s wife’s age is of 4/5 of Rohan’s age and Rohan’s age is of3/ 5 of Rohan’s father’s age. Find the age of Rohan’s son, if Rohan’s father is 50 years old? (a) 6 years (b) 8 years (c) 10 years (d) 12 years Explanation: Rohan’s father’s age = 50 years, Rohan’s age = (35×50)years = 30 years Rohan’s wife’s age = (45×30)years = 24 years Rohan’s son’s age = (13×24)years = 8 years |
9. Rohan’s son’s age is 1/3 of Rohan’s wife’s age. Rohan’s wife’s age is of 4/5 of Rohan’s age and Rohan’s age is of3/ 5 of Rohan’s father’s age. Find the age of Rohan’s son, if Rohan’s father is 50 years old? (a) 6 years (b) 8 years (c) 10 years (d) 12 years Explanation: Rohan’s father’s age = 50 years, Rohan’s age = (35×50)years = 30 years Rohan’s wife’s age = (45×30)years = 24 years Rohan’s son’s age = (13×24)years = 8 years |
10. Rayyan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rayyan’s sister was 10 years younger to him at the time of his marrige. The age of Rayyan’s sister is = ? (a) 32 years (b) 38 years (c) 36 years (d) 40 years Explanation: Let Rayyan’s age 8 years ago be x years, Then, present age = (x + 8) years ∴x+8=65x⇒5x+40=6x⇒x=40 Rayyan’s sister’s age 8 years ago = (40 – 10) years = 30 years ∴ His sister’s age now = (30+8) years = 38 years |
10. Rayyan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rayyan’s sister was 10 years younger to him at the time of his marrige. The age of Rayyan’s sister is = ? (a) 32 years (b) 38 years (c) 36 years (d) 40 years Explanation: Let Rayyan’s age 8 years ago be x years, Then, present age = (x + 8) years ∴x+8=65x⇒5x+40=6x⇒x=40 Rayyan’s sister’s age 8 years ago = (40 – 10) years = 30 years ∴ His sister’s age now = (30+8) years = 38 years |