Percentage
- In an election between two candidates A and B, A got 65% of the total votes cast and won the election by 2748 votes. Find the total number of votes cast if no vote is declared invalid.
-
View Hint View Answer Discuss in Forum
Let the total number of votes cast = x.
Number of votes got byA = 65 x ............(i) 100
⇒ B got= x – 65 x = 100x - 65x = 65 x 100 100 100
A won the election by 2748 votes.
∴ Number of votes for A= 35 x + 2748 ............(ii) 100
Form equations (i) and (ii),⇒ 65 x = 35 x + 2748 100 100 ⇒ 30x = 2748 100 ⇒ x = 2748 × 100 = 9160 30
∴ Total number of votes cast = 9160Correct Option: A
Let the total number of votes cast = x.
Number of votes got byA = 65 x ............(i) 100
⇒ B got= x – 65 x = 100x - 65x = 65 x 100 100 100
A won the election by 2748 votes.
∴ Number of votes for A= 35 x + 2748 ............(ii) 100
Form equations (i) and (ii),⇒ 65 x = 35 x + 2748 100 100 ⇒ 30x = 2748 100 ⇒ x = 2748 × 100 = 9160 30
∴ Total number of votes cast = 9160
- In an examination, 40% marks are required to pass. A obtains 10% less than the number of marks required to pass. B obtains
11 1 % less than A and C, 9 41 3 17
per cent less than the number of marks obtained by A and B together. Marks obtained by C is
-
View Hint View Answer Discuss in Forum
Suppose the maximum marks = 100
∴ Marks required to pass = 40
∵ A gets 10% less than pass marks.
∴ Marks secured byA = 40 × 90 = 36 100 ∵ B gets 11 1 % marks less than A. 9
∴ Marks secured dy B36 × 
100 - 11 1 
= 9 100 36 × 900 - 100 = 9 100 = 36 × 800 × 1 = 32 9 100
Total marks obtained by A and B
= 36 + 32 = 68∵ C gets 41 3 % 17
marks less than the marks obtained by A and B together.
∴ C’s marks68 × 100 - 41 3 = 17 100 68 × 100 - 700 = 17 100 68 × 1000 = 17 100 = 68 × 1000 × 1 = 40 17 100 Correct Option: B
Suppose the maximum marks = 100
∴ Marks required to pass = 40
∵ A gets 10% less than pass marks.
∴ Marks secured byA = 40 × 90 = 36 100 ∵ B gets 11 1 % marks less than A. 9
∴ Marks secured dy B36 × 100 - 11 1 = 9 100 36 × 900 - 100 = 9 100 = 36 × 800 × 1 = 32 9 100
Total marks obtained by A and B
= 36 + 32 = 68∵ C gets 41 3 % 17
marks less than the marks obtained by A and B together.
∴ C’s marks68 × 100 - 41 3 = 17 100 68 × 100 - 700 = 17 100 68 × 1000 = 17 100 = 68 × 1000 × 1 = 40 17 100
- A reduction of 25% in the price of apples would enable a purchaser to get 2 kg apples more for Rs. 240. Find the original price per kg of apples.
-
View Hint View Answer Discuss in Forum
Let the original price be ₹ x per kg
Reduction in price = ₹ 25 x 100 ∴ Reduced price = x – 25 x 100 = 75 x ..............................(i) 100
With ₹ 240, purchaser can purchase 2 kg more apples.
Now, 25% of 240= 25 × 240 = ₹ 60 100
⇒ Reduced price of 2 kg of apples = Rs. 60
∴ Reduced price of 1 kg of apples = 30 ............. (ii)
From equations (i) and (ii),= 75 × x = 30 100 ⇒ x = 30 × 100 = ₹ 40 75
The original price of 1 kg apples = Rs. 40Correct Option: C
Let the original price be ₹ x per kg
Reduction in price = ₹ 25 x 100 ∴ Reduced price = x – 25 x 100 = 75 x ..............................(i) 100
With ₹ 240, purchaser can purchase 2 kg more apples.
Now, 25% of 240= 25 × 240 = ₹ 60 100
⇒ Reduced price of 2 kg of apples = Rs. 60
∴ Reduced price of 1 kg of apples = 30 ............. (ii)
From equations (i) and (ii),= 75 × x = 30 100 ⇒ x = 30 × 100 = ₹ 40 75
The original price of 1 kg apples = Rs. 40
- 10% of the soldiers of an army are killed in the battle. 10% of the remaining soldiers died of disease and 10% of the remaining men were disabled. Now only 729000 soldiers are left in the army. How many soldiers were there in all in the army in the beginning ?
-
View Hint View Answer Discuss in Forum
Let the total number of soldiers in all in the army in the beginning = 100.
∴ Number of soldiers killed in the battle= 10 × 100 = 10 100
∴ Remaining soldiers
= 100 – 10 = 90
Number of soldiers who died of disease= 10 × 90 = 9 100
∴ Remaining soldiers = 90–9= 81
Number of disabled soldiers= 10 × 81 = 81 100 10
∴ Remaining soldiers= 81 – 81 = 810 - 81 = 729 10 10 10 ∴ If 729 soldiers are left, 10
hen total number of soldiers = 100
∴ If 1 soldier is left, then total number of soldiers= 100 × 10 729
∵ If 729000 soldiers are left, then total number of soldiers= 100 × 10 × 729000 = 1000000 729 Correct Option: D
Let the total number of soldiers in all in the army in the beginning = 100.
∴ Number of soldiers killed in the battle= 10 × 100 = 10 100
∴ Remaining soldiers
= 100 – 10 = 90
Number of soldiers who died of disease= 10 × 90 = 9 100
∴ Remaining soldiers = 90–9= 81
Number of disabled soldiers= 10 × 81 = 81 100 10
∴ Remaining soldiers= 81 – 81 = 810 - 81 = 729 10 10 10 ∴ If 729 soldiers are left, 10
hen total number of soldiers = 100
∴ If 1 soldier is left, then total number of soldiers= 100 × 10 729
∵ If 729000 soldiers are left, then total number of soldiers= 100 × 10 × 729000 = 1000000 729
- From the salary of an officer 10% is deducted as house rent; 15% of the rest he spends on children’s education; 10% of the balance he spends on clothes. After this expenditure, he is left with ₹ 2754. Find his salary.
-
View Hint View Answer Discuss in Forum
Let the salary be ₹100. Then,
House rent = ₹10; Balance = ₹(100 – 10) = ₹90.
Expenditure on children’s education = 15% of ₹90= 15 × 90 = ₹ 27 100 2 Balance now = 90 - 27 2 = 180 - 27 = ₹ 153 2 2
Expenditure on clothes= 10% of 153 = ₹ 153 2 20
Now, balance= 153 - 153 = ₹ 1377 2 20 20 If last balance is ₹ 1377 . then salary = ₹100. 20
If last balance is ₹ 2754, then salary= ₹ 100 × 20 × 2754 = ₹ 4000. 1377 Correct Option: B
Let the salary be ₹100. Then,
House rent = ₹10; Balance = ₹(100 – 10) = ₹90.
Expenditure on children’s education = 15% of ₹90= 15 × 90 = ₹ 27 100 2 Balance now = 90 - 27 2 = 180 - 27 = ₹ 153 2 2
Expenditure on clothes= 10% of 153 = ₹ 153 2 20
Now, balance= 153 - 153 = ₹ 1377 2 20 20 If last balance is ₹ 1377 . then salary = ₹100. 20
If last balance is ₹ 2754, then salary= ₹ 100 × 20 × 2754 = ₹ 4000. 1377
