Elitmus Previous Years Questions Profit & Loss And Ratio & Proportion

Profit & Loss And Ratio & Proportion

SET 1

1. A man buys spirit at Rs 60 per litre, adds water to it and then sells at Rs 75  per litre. What is the ratio of spirit to water if his profit in the deal is 37.5%?
(a) 9: 1
(b) 10: 1
(c) 11: 1
(d) None of these
2.  A cask contains a mixture of 49 litres of wine and water in the proportion 5:2. How much water must be added to it so that the ratio of wine to water may be 7:4?
(a) 3.5
(b) 6
(c) 7
(d) None of these
3.A milkman mixes 20L of water with 80L of milk. After selling one-fourth of this mixture, he adds a water to replenish the quantity that he has sold. What is the current proportion of water to milk?
(a) 2: 3
(b) 1: 2
(c) 1: 3
(d) 3: 4
4. The marked price of a table is Rs. 1200, which is 20% above the cost price. It is sold at a discount of 10% on the marked price. Find the profit percent.
(a) 10%
(b) 8%
(c) 7.5%
(d) 6%
5. A dealer buys dry fruits at Rs 100, Rs 80 and Rs 60 per kilogram. He mixes them in the ratio 3: 4: 5 by weight and sells at a profit of 50%. At what price per kilogram does he sell the dry fruit?
(a) Rs 80
(b) Rs 100
(c) Rs 95
(d) None of these
6. Mayank, Mirza, Little and Jaspal bought a motorbike for $60,000. Mayank paid one-half of the sum of the amounts paid by the other boys, Mirza paid one-third of the sum of the amounts paid by the other boys; and Little paid one fourth of the sum of the amounts paid by the other boys. How much did Jaspal has to pay?
(a) $15,000
(b) $13,000
(c) $17,000
(d) None of these
7.The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ration 1 : 2 : 3 : 4. When the pieces were sold, the merchant got Rs 70,000 less. Find the original price of the diamond?
(a) Rs 1.4 lakh
(b) Rs. 2 lakh
(c) Rs 1 lakh
(d) Rs 2.1 lakh
8. Two oranges, three bananas and four apples cost Rs 15. Three oranges, two bananas and one apple cost Rs 10. I bought 3 oranges, 3 bananas and 3 apples. How much did I pay?
(a) Rs 10
(b) Rs 8
(c) Rs 15
(d) Cannot be determined.
9. Instead of a metre scale, a cloth merchant uses a 120 cm scale while buying, but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment, what is his overall profit percentage?
(a) 20%
(b) 25%
(c) 40%
(d) 15%
10. I have one rupees coins, fifty paise coins and twenty five paise coins. The number of coins are in the ratio 2.5 : 3 : 4. If total amount with me is Rs 210, find the number of one  rupee coins ?
(a) 90
(b) 85
(c) 100
(d) 105
1.
Profit and Loss Ratio and Proportion -02-solution-05
2. Initial wine= 35 litres
Initial water = 14 litres
Since we want to create 7: 4 mixture of wine and water by adding only water, it means that the amount of wine is constant at 35 litres.
Thus, 7 : 4 = 35 : 20
Hence, water required is 6 litres.
3.As one-fourth of the solution (milk + water = 80L + 20L ) is sold, solution drawn out of it is 100 x (1/4)= 25 L
Quantity of the milk drawn out = 25 x (4/5)= 20 L
» Quantity of water drawn out= 5L
Now adding  25 L of water, quantity of water = 20 – 5 + 25 = 40L
Also, quantity of milk remaining= 80 – 20 = 60L
Required ratio= 40 : 60= 2 : 3
(a)
4. 20% increase for 100% is 120 and then 10 % decrease is 108%.
5. Cost price of ( 3 + 4 + 5 )= 12Kg of fruits Rs.( 300 + 320 + 300)= Rs. 920
SP at a profit of 50% = Rs. 1380
SP of fruits per kg= 1380/12= Rs. 115
6. Mayank paid 1/2 of the sum paid by the other three. Let the other three paid  $x jointly, then Mayank paid x/2.
So, x + x/2 = 60000 i.e. x = 40000. Hence Mayank paid $20, 000.
Likewise, Mirza and little paid $15000 and $12000 respectively.
Hence, amount paid by Jaspal  $(60, 000)-(20,000 + 15,000 + 12,000)=13,0007. Let the weight of the diamond be 10x, then price the diamond will be k(10)2=k.100×2 where k is a constant.
Weight of each piece= x, 2x, 3x and 4x
Therefore, their price will be kx2, k4x2, k9x2 and k16x2
Total price of pieces = kx2(1 + 4 + 9 + 16) = 30kx2
Given,
k.100.×2- k.30.×2= 70,000 or kx2=1,000
» Original price of diamond
=k.100.×2 = 100 x 100=1,00,0008. 2O + 3B + 4A = 15   —- (1)
3O + 2B + A = 10     —- (2)
Adding equation (i) and (ii), we get
5O + 5B + 5A = 25 or O + B + A = 5
» 3O + 3B + 3A = 3 x 5 = 15
(c)

9. Let the price of 100 cm of cloth be Rs 100, but he gets 120 cm of cloth for Rs 100. Hence, his actual cost for 1 cm = 100/120= Rs. 5/6
Now, instead of selling 100 cm, by cheating he sells 80 cm of cloth for the cost price of 100 cm of cloth.
To calculate his profit, the cost price of 80 cm of cloth = 5/6 X 80= Rs. 66.66
Selling Price of 80 cm of cloth(actually 100 cm for the buyes) at a discount of 20%.
= 100 x 0.8= Rs. 80
Hence Profit Percentage= (80-66.66) x 100/66.66 = 20.02%
or 20 % approx.

10. Ratio of number of one rupee, fifty paisa, twenty five paisa coins= 2.5 : 3 : 4
» Ratio of value of coins= 2.5 x 1 : 3/2 : 4/4  »  5 : 3 : 2
Let amount of Rs 1 coins, 50 paisa coins and 25 paisa coins be 5x, 3x and 2x respectively.
So, 5x + 3x + 2x = 210(given)
Hence, x=21
»Value of one rupee coins = number of one rupees coins = 21 x 5=105