Every month a man consumes 25 kg rice and 9 kg wheat. The price of rice is 20% of the price of wheat and thus he spends total Rs. 350 on the rice and wheat per month. If the price of wheat is increased by 20% then what is the percentage reduction of rice consumption for the same expenditure of Rs. 350? Given that the price of rice and consumption of wheat is constant :
(A) 40%
(B) 25%
(C) 36%
(D) 24%
Solution:
Let the price of wheat is x per kg. Then price of wheat will be 5x per kg. Expenditure on rice = 25 × x = 25x Expenditure of wheat = 9 × 5x = 45x Total cost, 25x + 45x = 350 70x = 350 x = 5 Hence, price of Rice = Rs. 5 per kg. Price of wheat = 25 per kg. Now, price of wheat = 25 ---- 20% ↑----> Rs. 30 per kg. Let the new amount of rice is N kg, then N*5 + 9*30 = 350 N = 16 kg. % decrease in the amount of rice $$\eqalign{ & = \frac{{\left( {25 - 16} \right) \times 100}}{{25}} \cr & = 36\% \cr} $$
If the numerator of a fraction is increased by 15% and denominator is decreased by 20%, then the fraction, so obtained, is $$\frac{{17}}{{65}}.$$ ÃÂÃÂ What is the original fraction?
A man spend $$7\frac{1}{2}$$% of his money and after spending 75% of the remaining he had Rs. 370 left. How much money did he have :
(A) 1200
(B) 1600
(C) 1500
(D) 1400
Solution:
Let the 100unit is the salary of the person After spending 7.5% of his salary remain salary 92.5 Now again he spended 75% of 92.5 and remain 25% which have value Rs. 370 According to the question, 92.5 × 25% unit = 370 92.5 × $$\frac{1}{4}$$ unit = 370 1 unit = $$\frac{370 × 4}{92.5}$$ 100 unit = $$\frac{370 × 4 × 100}{92.5}$$ = Rs. 1600
35.
A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
(A) 45%
(B) $$45\frac{5}{{11}}\% $$
(C) $$54\frac{6}{{11}}\% $$
(D) 55%
Solution:
Number of runs made by running = 110 - (3 x 4 + 8 x 6) = 110 - (60) = 50 ∴ Required percentage $$\eqalign{ & = \left( {\frac{{50}}{{110}} \times 100} \right)\% \cr & = 45\frac{5}{{11}}\% \cr} $$
36.
A fruit seller sells 45% of the oranges that he has along with one more orange to a customer. He then sells 20% of the remaining oranges and 2 more oranges to a second customer. He then sells 90% of the now remaining oranges to a third customer and is still left with 5 oranges. How many oranges did the fruit seller have initially?
If radius of a circle is increased by 5%, then the increase in it's area is :
(A) 10.25%
(B) 5.75%
(C) 10%
(D) 5%
Solution:
Quicker approach $$ \uparrow $$ in A = a + b + $$\frac{ab}{100}$$ Here a = b = 5% $$ \uparrow $$ in A : $$\eqalign{ & = \left( {5 + 5 + \frac{{5 \times 5}}{{100}}} \right)\% \cr & = 10.25\% \cr} $$
38.
Rita's income is 15% less than Richa's income. By what percent is Richa's income more than Rita's income?
The marked price of an article is Rs. 2400. The shopkeeper gives successive discounts of x% and 15% to the customer. If the customer pays Rs. 1876.80 for the article, find the value of x :
(A) 9%
(B) 8%
(C) 12%
(D) 11%
Solution:
Marked price of an article = Rs. 2400 According to the question, 2400 × (100 - x)% of 85% = 1876.80 ⇒ 2400 × $$\frac{100 - x}{100}$$ × $$\frac{85}{100}$$ = 1876.80 ⇒ (100 - x) = $$\frac{1876.80 × 100 × 100}{2400 × 85}$$ ⇒ (100 - x) = $$\frac{18768000}{204000}$$ ⇒ (100 - x) = 92 ⇒ x = 100 - 92 ⇒ x = 8%