**Decimals & Fractions Practice Problems: Level 01**

**1. Rashi spends 1/7th of his income on clothes,1/5th of the remaining on entertainment, 1/3rd of the remaining on books . If she still has Rs. 4800 with her, find her total income**

A. 11025

B. 12025

C. 10500

D. 45256

**Sol : Option C**

Just concentrate on the remaining part at every step. Firstly she spends 1/7th of his income, implies he is left with 6/7th of his income. Then he spends 1/5th of that, means he saves 4/5th of that. After this she spends 1/3rd of the remaining, means he saves 2/3rd of that. In total she saves 2/3rd of 4/5th of 6/7th i.e. 2/3 × 4/5 × 6/7 of the total which is given to be 4800. Now 48/105 x = 4800 i.e. x = Rs. 10500.

**2. Find the fractional equivalent of
**

A. 5209/16665

B. 5219/16665

C. 5239/16665

D. 5211/16665

**Sol : Option A**

As it is case of mixed recurring

**3. Find the fractional equivalent of**

A. 1421/1111

B. 421/1111

C. 4211/1111

D. 419/1111

**Sol : Option B**

As it is case of pure recurring.

**4. Find the fractional equivalent of**

A. 5111/9000

B. 6117/9000

C. 6119/9000

D. None of these

**Sol : Option D**

**5. After spending 3/4 of his income a man is left with Rs. 100.Find his total income.**

A. 400

B. 200

C. 75

D. None of these

**Sol : Option A**

After spending 3/4th of the income, he will be left with 1/4th of the income and that is given to be Rs. 100, thus ¼ of income is 100. So income = 100 * 4/1 = 400

**6. Ravi spends 2/9th of his income, then he spends3/7th of the remaining. If he still has Rs. 140 with him. Find his total income.**

A. 315

B. 3150

C. 1175

D. 6130

**Sol : Option A**

7/9 of 4/7 of income = 140. 4/9 of income = 140 ⇒ income = 140 x 9/4 = 315

**7. In a library 2/3 of books are in English and the remaining 300 are of Hindi. Find the total books in library**

A. 400

B. 900

C. 275

D. None of these

**Sol : Option B**

2/3 of books are in English means remaining 1 – (2/3) = 1/3 are in Hindi which is equal to 300. So 1/3rd of total = 300 ⇒ Total books = 300 x 3 = 900.

**8 Find the fractional equivalent of**

A. 221/1650

B. 227/1650

C. 223/1650

D. None of these

**Sol : Option C**

As it is case of mixed recurring = (1351 – 13) /9900 = 1338/9900 = 223/1650.

**9. Raju has some money. He gave 1/9 of it to his son Ramu and 2/3rd of remaining to his daughter Geeta. He still has Rs. 200 left. How much money he had initially.**

A. 6400

B. 200

C. 675

D. None of these

**Sol : Option C**

As he gave 1/9 to his son Ramu so he is left with 1 – (1/9) = 8/9. Now out of 8/9 he gives 2/3 to his daughter so he is left with 1/3 of 8/9. so we will solve as follows: 8/9 of 1/3 of x = 200. x = 200 x 9 x 3/8 = 675.

**10. Find the fractional equivalent of**

A. 967/4995

B. 968/4995

C. 1968/4995

D. None of these

**Sol : Option B**

As it is case of mixed recurring

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