# Solved Examples

(First work out the sum and then look at solutions below to assess your method)
1. Ramu had three notebooks X, Y, Z. Of these, X had 120 pages. Y had 10% more and Z 10% pages less. If he tore roughly 5%, 10%,
15% of pages in X, Y and Z respectively, then what % of pages did he tear out?
1. 8%                2. 10%               3. 7%              4. 13%

2. Rohan had scored 70% more in Maths than in Science. However, the science paper was for 50 marks and Maths for 150. If Rohan got
81 marks in both subjects, what was his % in Science & Maths?
1. 34%; 60%                2. 36%; 54%            3. 54%; 36%           4. 60%; 34%

3. Raj Kumar was late 60% of all school days. Of the remaining he was absent 35% of the days. If school was for 325 days how many
days did he reach on time?
1. 85              2. 16                   3. 62              4. 45

4. Roy drove at a speed 30% greater than usual outside the city limits. If he normally drove at 60 kmph in the city, then how long did he
take to do a 624 km stretch on the highway?
1. 20.8 hrs             2. 8 hrs             3. 10.4 hrs           4. 7.3 hrs

5. A man donated 5% of his income to a charitable organisation and deposited 20% of the remainder in a bank. If he now has Rs 1919
left, what is his income?
1.    Rs 2558.60        2. Rs 2525       3. Rs 2500      4. Rs 2300

6. He was late for 60%(325) = 195 days. Remaining days = 325 â€“ 195 = 130.
He was absent of 35% remaining days means that he was on time for 65% days.
Hence 65%(130) = 85 is the answer.

7. Highway speed = 60 Ã— 1.30 = 78. Hence time taken = D/S = 624/78 = 8.

He deposits 20%(95) = 19 in the bank, so he has 76 left.
But since he has 1919 left, the original amount was 1919 Ã— 100/76 = 2525.

9. 2/5% = 2/5 Ã· 100 = 2/500 = 1/250.

10. Let the price be 100. Reduced price = 90. To restore it, we must increase 90 by 10, i.e. 10/90 Ã— 100 = 11 1/9%. Short cut method is to
use the formula.

11. Percentage increase from 4 to 5 is 25%. Hence slump in business is 20% (see box on percentage increase/decrease above).

12. Total requirement = 50%(180 + 150) = 165.
In First paper he gets = 30%(180) = 54.
So marks required in second paper = 165 â€“ 54 = 111.
Required Percentage = 111/150 Ã— 100 = 74%.

13. Starting from the back, we have: C = 2000, so 10% of B = 20%(2000) = 400, hence B = 4000.
Again, 5% of A = 15%(4000) = 600, hence A = 12000.
Total = 12000 + 4000 + 2000 = 18000.