5. On selling mangoes at 36 for a rupee, a shopkeeper loses 10%. How many mangoes should he sell for a rupee in order to gain 8%?
a. 25
b. 30
c. 35
d. 40
Answer: B
Explanation:
Selling price of 1 apple = Rs.$\dfrac{1}{{36}}$
$CP\left( {1 - L\% } \right) = SP$
$ \Rightarrow CP\left( {1 - 10\% } \right) = \dfrac{1}{{36}}$
$ \Rightarrow CP\left( {1 - \dfrac{{10}}{{100}}} \right) = \dfrac{1}{{36}}$
$ \Rightarrow CP\left( {\dfrac{{90}}{{100}}} \right) = \dfrac{1}{{36}}$
$ \Rightarrow CP = \left( {\dfrac{1}{{36}} \times \dfrac{{100}}{{90}}} \right)$
In order to gain 8%, selling price of mangoes $ \Rightarrow$ $SP = CP\left( {1 + P\% } \right)$
$ \Rightarrow SP = \left( {\dfrac{1}{{36}} \times \dfrac{{100}}{{90}}} \right)\left( {1 + \dfrac{8}{{100}}} \right)$
$ \Rightarrow \require{cancel}\Rightarrow SP = \left( {\dfrac{1}{\cancel{36}} \times \dfrac{\cancel{100}}{{90}}} \right)\left( {\dfrac{\cancel{108}^3}{\cancel{100}}} \right)$
$ \Rightarrow SP = \dfrac{1}{{30}}$
$\therefore $ For one rupee, he should sell 30 mangoes.
6. A boy buys eggs at 10 for Rs.1.80 and sells them at 11 for Rs. 2. What is his gain or loss per cent?
a. 1.27%
b. 1.01%
c. 1.68%
d. 1.77%
Answer: B
Explanation:
To avoid fractions, let the number of eggs purchased be, LCM of 10 and 11 = 110
CP of 110 eggs = $\dfrac{{110 \times 1.80}}{{10}}$ $= Rs. 19.80$
SP of 110 eggs = $\dfrac{{110 \times 2.0}}{{11}}$ $= Rs. 20.00$
Profit per cent = $\dfrac{{20 - 19.80}}{{19.80}} \times 100$ = $\dfrac{1}{{99}} \times 100$ $= 1.01\%$
7. A woman buys apples at 15 for a rupee and the same number at 20 a rupee. She mixes and sells them at 35 for 2 rupees. What is her gain per cent or loss per cent?
a. 2.04%
b. 3.5%
c. 4.4%
d. 5.4%
Answer: A
Explanation:
Suppose the woman buys two lots of (LCM of 15, 20 and 35) = 420 apples.
One apple cost from the first lot = $\dfrac{1}{{15}}$.
420 apples cost = $\dfrac{1}{{15}} \times 420 = 28$
One apple cost from the second lot = $\dfrac{1}{{20}}$.
420 apples cost = $\dfrac{1}{{20}} \times 420 = 21$
Total cost for 840 apples $= 28 + 21 = Rs. 49$ $- - (1)$
Selling price of 1 apple = $\dfrac{2}{{35}}$.
840 apples selling price = $\dfrac{2}{{35}} \times 840 = 48$ $- - (2)$
Loss per cent = $\dfrac{{49 - 48}}{{49}} \times 100 = 2.04\% $
8. Some quantity of coffee is sold at Rs. 22 per kg, making 10% profit. If total gain is Rs. 88, what is the quantity of coffee sold?
a. 44
b. 55
c. 60
d. 70
Answer: A
Explanation:
$CP\left( {1 + P\% } \right) = SP$
$ \Rightarrow CP\left( {1 + 10\% } \right) = 22$
$ \Rightarrow CP\left( {1 + \dfrac{{10}}{{100}}} \right) = 22$
$ \Rightarrow CP\left( {\dfrac{{110}}{{100}}} \right) = 22$
$ \Rightarrow CP = 22 \times \dfrac{{100}}{{110}} = 20$
Profit on one kg of coffee $= 22 - 20 = Rs.2$
Let $x$ kgs of coffee sold. So total profit = $2x$.
$ \Rightarrow 2x = 88$
$ \Rightarrow $ $x = 44$
