Due to fall of 10% in the rate of sugar, 500 gm more sugar can be purchased for Rs. 140. Find the original rate?
(A) Rs. 31.11
(B) Rs. 29.22
(C) Rs. 33.11
(D) Rs. 32.22
Solution:
Money spent originally = Rs. 140 Less Money to be spent now = 10% of 140 = Rs. 14 Rs. 14 now yield 500 gm sugar So, Present rate of sugar = Rs. 28 per kg. If the present value is Rs. 90, the original value = Rs. 100 If the present value is Rs. 28 the original value $$ = {\text{Rs}}{\text{. }}\frac{{100}}{{90}} \times 28 = {\text{Rs}}{\text{. }}31.11$$
2.
The length of a rectangle is increased by 10% and breadth decreased by 10% Then the area of the new rectangle is :
(A) Neither decreased nor increased
(B) Increased by 1%
(C) Decreased by 1%
(D) Decreased 10%
Solution:
Decrease in area $$\eqalign{ & = \frac{{{x^2}}}{{100}}\% \cr & = \frac{{{{\left( {10} \right)}^2}}}{{100}} \cr & = 1\% \cr} $$
3.
A bag contains 600 coins of 25p denomination and 1200 coins of 50p denomination. If 12% of 25p coins and 24% of 50p are removed, the percentage of money removed from the bag is nearly :
In a hotel, 60% had vegetarian lunch while 30% had non-vegetarian lunch and 15% had both types of lunch. If 96 people were present, how many did not eat either type of lunch ?
(A) 20
(B) 24
(C) 26
(D) 28
Solution:
$$\eqalign{ & n\left( A \right) = \left( {\frac{{60}}{{100}} \times 96} \right) = \frac{{288}}{5} \cr & n\left( B \right) = \left( {\frac{{30}}{{100}} \times 96} \right) = \frac{{144}}{5} \cr & n\left( {A \cap B} \right) = \left( {\frac{{15}}{{100}} \times 96} \right) = \frac{{72}}{5} \cr & \therefore n\left( {A \cup B} \right): \cr & = n\left( A \right) + n\left( B \right) - n\left( {A \cap B} \right) \cr & = \frac{{288}}{5} + \frac{{144}}{5} - \frac{{72}}{5} \cr & = \frac{{360}}{5} \cr & = 72 \cr} $$ So, people who had either or both types of lunch = 72 Hence, people who had neither type of lunch = (96 - 72) = 24
A man spends a part of his monthly income and saves the rest. The ratio of his expenditure to the saving is 61 : 6. If his monthly income is Rs. 8710, the amount of his monthly savings is :
(A) Rs. 870
(B) Rs. 690
(C) Rs. 980
(D) Rs. 780
Solution:
Expense + Saving = Income 61 + 6 = 67 67 units = Rs. 8710 1 unit = $$\frac{{8710}}{{67}}$$ = 130 6 unit = Rs. 780
7.
If 75% of a number is added to 75, then the result is the number itself. The number is :
(A) 50
(B) 60
(C) 300
(D) 400
Solution:
Let the number be x Then, 75% of x + 75 = x ⇔ x - $${\frac{{75}}{100}}$$ x = 75 ⇔ x - $${\frac{{3}}{4}}$$ x = 75 ⇔ $${\frac{{x}}{4}}$$ = 75 ⇔ x = 300
8.
In an election, a total of 500000 voters participated. A candidate got 255000 votes which was 60% of total valid votes. What was the percentage of invalid votes :
(A) 10%
(B) 12%
(C) 15%
(D) $$\frac{300}{17}$$%
Solution:
Let the number of valid votes be x Then, 60% of x = 255000 ⇒ x = $$\left( {\frac{{255000 \times 100}}{{60}}} \right)$$ ⇒ x = 425000 Number of invalid votes : = (500000 - 425000) = 75000 ∴ Required percentage : = $$\left( {\frac{{75000 \times 100}}{{500000}}} \right)$$ % = 15%
9.
A fraction in reduced form is such that when it is squared and then its numerator is increased by 25% and the denominator is reduced t0 80% it results in $$\frac{5}{8}$$ of original fraction. The product of the numerator and denominator is :
Salary of Mohit is 60% more than Vijay. Salary of Vijay is how much percent less than Mohit?
(A) 45%
(B) 42.5%
(C) 47.5%
(D) 37.5%
Solution:
Given: Salary of Mohit is 60% more than Vijay Formula used: Percentage = $$\frac{{{\text{Difference}}}}{{{\text{Larger value}}}} \times 100$$ Calculations: Let the salary of Vijay = Rs. 100 ⇒ So, the salary of Mohit = 100 + 60% of 100 = 100 + 60 = Rs. 160 According to the formula, $$\eqalign{ & \Rightarrow {\text{Percentage}} = \frac{{{\text{Difference}}}}{{{\text{Larger value}}}} \times 100 \cr & = \frac{{160 - 100}}{{160}} \times 100 \cr & = \frac{{60}}{{160}} \times 100 \cr & = 37.5\% \cr} $$ Hence, the salary of Vijay and less than Mohit by 37.5%