**Q.1 Present ages of Anu and Raj are in the ratio 4:5. Eight years from now the ratio of their ages will be 5:6. Find the present age of Raj ?**

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**A) 38 **

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**B) 39**

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**C) 40**

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**D) 41**

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**Ans. C**

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**Let the present ages of Anu and Raj be 4x years and 5x years respectively.**

**After eight years. Anu’s age = (4x + 8) years;**

**After eight years, Raj’s age = (5x + 8) years.**

**Therefore, the ratio of their ages after eight years =**

**4x + 8 / 5x + 8**

**This is given to be 5 : 6**

**Therefore,**

**4x + 8/ 5x + 8 = 5/6**

**Cross-multiplication gives 6 (4x + 8) = 5 (5x + 8)**

**or 24x + 48 = 25x + 40**

**or 24x + 48 – 40 = 25x**

**or 24x + 8 = 25x**

**or 8 = 25x – 24x**

**or 8 = x**

**Therefore, Anu’s present age = 4x = 4 × 8 = 32 years**

**Raj’s present age = 5x = 5 × 8 = 40 years**

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**Q.2 A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present age of Grandfather ?**

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**A) 50 yrs**

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**B) 60 yrs**

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**C) 61 yrs**

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**D) 62 yrs**

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**Ans. B**

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**Let the granddaughter’s age be x years. Therefore, grandfather’s age will be**

**10x years.**

**According to the question,**

**Grandfather’s age = Granddaughter’s age + 54 years**

**10x = x + 54**

**Transposing x to L.H.S, we obtain**

**10x – x = 54**

**9x = 54**

**x = 6**

**Granddaughter’s age = x years = 6 years**

**Grandfather’s age = 10x years = (10 × 6) years = 60 years**

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**Q.3 10 yrs ago the sum of the ages of two brothers was equal to one-third of the age of their father. Elder brother is 2yrs older than the younger . At present the sum of their ages is less than the age of the father by 14yrs. What is the age of the father ?**

**A) 46 yrs**

**B) 47 yrs**

**C) 48 yrs**

**D) 49 yrs**

**Ans. A**

**Let the age of father, elder son & younger son be x,y & z yrs**

**Therefore, y-10+z-10 = 1/3(x-10)**

**Or 3y-30+3z-30 = x-10**

**Or –x+3y+3z = 50—–i**

**y-z = 2—–ii**

**x-(y+z) = 14**

**x-y-z = 14—-iii**

**Multiply equation iii by 3 & then add equation I, we get**

**2x = 92**

**X=92/2 = 46**

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**Q.4 The age of the father 3yrs ago was 7 times the age of his son. At present the father’s age is five times that of his son. What are the present ages of the father & the son ?**

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**A) Father’s age=45 yrs , Son’s age=9 yrs**

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**B) Father’s age=46 yrs , Son’s age=10 yrs**

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**C) Father’s age=47 yrs , Son’s age=11 yrs**

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**D) Father’s age=48 yrs , Son’s age=12 yrs**

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**Ans. A**

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**Shortcut:**

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**Sons’s age = T1 (x-1) / (x-y)**

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**18/2 = 9 yrs**

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**In the same way, we have**

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**Father’s age = 45 yrs**

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**Q.5 Sum of the ages of the mother & her daughter is 50 yrs. Also 5 yrs ago, the mother’s age was 7 times the age of the daughter. What are the present ages of the mother & the daughter ?**

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**A) Mother’s age= 40 yrs. & Daughter’s age= 9 **

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**B) Mother’s age= 41 yrs. & Daughter’s age= 10 **

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**C) Mother’s age= 40 yrs. & Daughter’s age= 10 **

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**D) Mother’s age=39 & Daughter’s age=10 yrs.**

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**Ans. C**

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**Shortcut:**

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**Daughter’s age = S1+T1 (N1-1) / N1+1**

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**50+ 5(7-1) / 7+1**

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**10 yrs**

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**Or Mother’s age = 50-10 = 40 yrs**

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**NOTE: If there will be after…….years like”after 5 years” in place of ago like “5 yrs ago”, then use this formula:**

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**S1-T1(N-1) / N1+1**