TEST - 7
1. Ayesha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? (a) 2 years (b) 4 years (c) 6 years (d) 8 years Explanation: Mother’s age when Ayesha’s brother was born = 36 years. Father’s age when Ayesha’s brother was born = (38 + 4) years = 42 years. ∴ Required difference = (42 – 36) years = 6 years. |
1. Ayesha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? (a) 2 years (b) 4 years (c) 6 years (d) 8 years Explanation: Mother’s age when Ayesha’s brother was born = 36 years. Father’s age when Ayesha’s brother was born = (38 + 4) years = 42 years. ∴ Required difference = (42 – 36) years = 6 years. |
2. A person’s present age is two- fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present? (a) 32 years (b) 36 years (c) 40 years (d) 48 years Explanation: Let the mother’s present age be x years. Then, the person’s present age =2/5xyears ∴2/5x+8=1/2(x+8) ⇒ 2(2x+40) = 5(x+8) ⇒ x=40. |
2. A person’s present age is two- fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present? (a) 32 years (b) 36 years (c) 40 years (d) 48 years Explanation: Let the mother’s present age be x years. Then, the person’s present age =2/5xyears ∴2/5x+8=1/2(x+8) ⇒ 2(2x+40) = 5(x+8) ⇒ x=40. |
3. Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q’s age? (a) 1 years (b) 2 years (c) 25 years (d) Data is inadequate Explanation: 1. The difference of age b/w R and Q = The difference of age b/w Q and T. 2. Sum of age of R and T is 50 i.e. (R + T) = 50. Question: R – Q =? Explanation: R – Q = Q – T; (R + T) = 2Q Now given that, (R + T) = 50; So, 50 = 2Q and therefore Q = 25. Question is (R – Q) =? Here we know the value (age) of Q (25), but we don’t know the age of R. Therefore, (R-Q) cannot be determined. |
3. Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q’s age? (a) 1 years (b) 2 years (c) 25 years (d) Data is inadequate Explanation: 1. The difference of age b/w R and Q = The difference of age b/w Q and T. 2. Sum of age of R and T is 50 i.e. (R + T) = 50. Question: R – Q =? Explanation: R – Q = Q – T; (R + T) = 2Q Now given that, (R + T) = 50; So, 50 = 2Q and therefore Q = 25. Question is (R – Q) =? Here we know the value (age) of Q (25), but we don’t know the age of R. Therefore, (R-Q) cannot be determined. |
4. The age of father 10 years ago was thrice the age of his son. Ten years hence, father’s age will be twice that of his son. The ratio of their present ages is: (a) 5 : 2 (b) 7 : 3 (c) 9 : 2 (d) 13 : 4 Explanation: Let the ages of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] ⇒ 3x + 20 = 2x + 40 ⇒ x = 20 ∴ Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3 |
4. The age of father 10 years ago was thrice the age of his son. Ten years hence, father’s age will be twice that of his son. The ratio of their present ages is: (a) 5 : 2 (b) 7 : 3 (c) 9 : 2 (d) 13 : 4 Explanation: Let the ages of father and son 10 years ago be 3x and x years respectively. Then, (3x + 10) + 10 = 2[(x + 10) + 10] ⇒ 3x + 20 = 2x + 40 ⇒ x = 20 ∴ Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3 |
5. The ages of Noman and Waqas are in the ratio 6: 5 respectively. After 9 years the ratio of their ages will be 9: 8. What is the difference in their ages now? (a) 3 years (b) 5 years (c) 7 years (d) 9 years Explanation: Let Noman’s age be 6x years, Then waqas’s age = 5x years ∴6x+95x+9=98⇒8 (6x+9) = 9(5x+9) ⇒ 48x−45x=81−72⇒3x=9⇒x=3 Difference in their ages = (6x−5x) = x years=3 years. |
5. The ages of Noman and Waqas are in the ratio 6: 5 respectively. After 9 years the ratio of their ages will be 9: 8. What is the difference in their ages now? (a) 3 years (b) 5 years (c) 7 years (d) 9 years Explanation: Let Noman’s age be 6x years, Then waqas’s age = 5x years ∴6x+95x+9=98⇒8 (6x+9) = 9(5x+9) ⇒ 48x−45x=81−72⇒3x=9⇒x=3 Difference in their ages = (6x−5x) = x years=3 years. |
6. The ages of Shoaib and Kamal are in the ratio of 8: 7 respectively. After 10 years, the ratio of their ages will be 13: 12. What is the difference between their ages? (a) 2 years (b) 4 years (c) 8 years (d) 6 years Explanation: Let Shoaib’s age be 8x years, Then Kamal’s age = 7x years ∴8x+107x+10=1312⇒12(8x+10)=13(7x+10)⇒96x+120=91x+130⇒5x=10⇒x=2 Difference between their ages =(8x−7x)= x years = 2years |
6. The ages of Shoaib and Kamal are in the ratio of 8: 7 respectively. After 10 years, the ratio of their ages will be 13: 12. What is the difference between their ages? (a) 2 years (b) 4 years (c) 8 years (d) 6 years Explanation: Let Shoaib’s age be 8x years, Then Kamal’s age = 7x years ∴8x+107x+10=1312⇒12(8x+10)=13(7x+10)⇒96x+120=91x+130⇒5x=10⇒x=2 Difference between their ages =(8x−7x)= x years = 2years |
7. The ages of A and B are in the ratio 6: 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years? (a) 7 : 6 (b) 8 : 7 (c) 9 : 8 (d) 3 : 4 Explanation: A’s age = (44×611)years = 24 years And B’s age = (44−24)years = 20 years Ratio of their ages after 8 years = (24+8)(20+8)=3228=87=8:7 |
7. The ages of A and B are in the ratio 6: 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years? (a) 7 : 6 (b) 8 : 7 (c) 9 : 8 (d) 3 : 4 Explanation: A’s age = (44×611)years = 24 years And B’s age = (44−24)years = 20 years Ratio of their ages after 8 years = (24+8)(20+8)=3228=87=8:7 |
8. Farah got married 8 years ago, Today her age is 1 .2/ 7 times her age at the time of her marriage. At present her daughter’s age is one- sixth of her age. What was her daughter’s age 3 years ago? (a) 4 years (b) 3 years (c) 6 years (d) none of these Explanation: Let Farah’s age 8 years ago be x years. Then , her present age = (x + 8) ∴x+8=97x⇒7x+56=9x⇒2x=56⇒x=28 ∴ Farah’s age now = (x + 8) years = (28 + 8) years = 36 Her daughter’s age now =(16×36) years = 6 years Her daughter’s age 3 years ago = (6 – 3) years = 3 years |
8. Farah got married 8 years ago, Today her age is 1 .2/ 7 times her age at the time of her marriage. At present her daughter’s age is one- sixth of her age. What was her daughter’s age 3 years ago? (a) 4 years (b) 3 years (c) 6 years (d) none of these Explanation: Let Farah’s age 8 years ago be x years. Then , her present age = (x + 8) ∴x+8=97x⇒7x+56=9x⇒2x=56⇒x=28 ∴ Farah’s age now = (x + 8) years = (28 + 8) years = 36 Her daughter’s age now =(16×36) years = 6 years Her daughter’s age 3 years ago = (6 – 3) years = 3 years |
9. The age of a mother today is thrice that of her daughter. After 12 years, the age of the mother will be twice that of her daughter. The present age of the daughter is? (a) 12 years (b) 14 years (c) 16 years (d) 18 years Explanation: Let the daughter’s age be x years. Then, mother age = 3x years 3x + 12 = 2 (x + 12) ⇒ 3x + 12 = 2x + 24 ⇒ x = 12 Present age of daughter = 12 years. |
9. The age of a mother today is thrice that of her daughter. After 12 years, the age of the mother will be twice that of her daughter. The present age of the daughter is? (a) 12 years (b) 14 years (c) 16 years (d) 18 years Explanation: Let the daughter’s age be x years. Then, mother age = 3x years 3x + 12 = 2 (x + 12) ⇒ 3x + 12 = 2x + 24 ⇒ x = 12 Present age of daughter = 12 years. |
10. The present age of Mr. Sohail is three times the age of his son. Six years hence, the ratio of their ages will be 5: 2. What is the present age of Mr. Sohail? (a) 48 years (b) 50 years (c) 54 years (d) 60 years Explanation: Let the son’s age be x years , Then Mr. Sohail’s age = 3x years ∴3x+6x+6=52⇒2(3x+6)=5(x+6)⇒6x+12=5x+30⇒x=18 ∴ Present age of Mr. Sohail= 3x years = (3 × 18) years = 54 years. |
10. The present age of Mr. Sohail is three times the age of his son. Six years hence, the ratio of their ages will be 5: 2. What is the present age of Mr. Sohail? (a) 48 years (b) 50 years (c) 54 years (d) 60 years Explanation: Let the son’s age be x years , Then Mr. Sohail’s age = 3x years ∴3x+6x+6=52⇒2(3x+6)=5(x+6)⇒6x+12=5x+30⇒x=18 ∴ Present age of Mr. Sohail= 3x years = (3 × 18) years = 54 years. |