# 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 = (31257 – 3)/99990 = 31254/99990 = 5209/16665.
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. = 3789/9999 = 421/1111.
4. Find the fractional equivalent of A. 5111/9000
B. 6117/9000
C. 6119/9000
D. None of these
Sol : Option D = (6789-678)/9000 = 6111/9000.
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 = (1937-1)/9990 = 968/4995.