BANK & INSURANCE (PROFIT LOSS AND DISCOUNT) PART 3

Total Questions: 70

31. The average cost price of 3 articles ‘A’, ‘B’ and ‘C’ is Rs. 920 and the average cost price of articles ‘A’ and ‘B’ is Rs. 960. Cost price of article ‘C’ is 5% more than that of article ‘A’. If articles ‘A’, ‘B’ and ‘C’ are sold at profit of 15%, loss of 10% and profit of Rs. 22, respectively, then find the average of their selling prices.

Correct Answer: (b) Rs. 930
Solution:

Sum of cost price of articles ‘A’, ‘B’ and ‘C’ = 920 × 3
= Rs. 2,760

Sum of cost price of articles ‘A’ and ‘B’ = 960 × 2
= Rs. 1,920

So, cost price of article ‘C’ = 2760 - 1920 = Rs. 840

Cost price of article ‘A’ = 840 ÷ 1.05 = Rs. 800
So, cost price of article ‘B’ = 1920 - 800
= Rs. 1,120

Selling price of article ‘A’ = 800 × 1.15 = Rs. 920
Selling price of article ‘B’ = 1120 × 0.9 = Rs. 1008
Selling price of article ‘C’ = 840 + 22 = Rs. 862

So, average of the selling prices of articles ‘A’, ‘B’ and ‘C’ = (920 + 1008 + 862) ÷ 3 = Rs. 930

32. Average of cost prices of articles ‘A’ and ‘B’ is Rs. 1200 and cost price of article ‘A’ is Rs. ___ than cost price of article ‘B’. If article ‘A’ is sold at a discount of __% after being marked 75% above its cost price while article ‘B’ is sold at a profit of 40%, then total profit earned is less than Rs. 1200 but more than Rs. 600.

The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true:
I. 480 less, 20
II. 800 more, 40
III. 400 more, 10

Correct Answer: (a) Only I
Solution:

For I:
Cost price of articles ‘A’ and ‘B’ together = 1200 × 2
= Rs. 2400

Cost price of article ‘A’ = (2400 - 480)/2 = Rs. 960
Cost price of article ‘B’ = 2400 - 960 = Rs. 1440

Selling price of both articles = 0.80 × 1.75 × 960 + 1.40 × 1440 = Rs. 3360

Profit earned = 3360 - 2400 = Rs. 600 < 960 < 1200
So, ‘I’ can be the answer.

For II:
Cost price of articles ‘A’ and ‘B’ together = 1200 × 2
= Rs. 2400

Cost price of article ‘A’ = (2400 + 800)/2 = Rs. 1600
Cost price of article ‘B’ = 2400 - 1600 = Rs. 800

Selling price of both articles = 0.60 × 1.75 × 1600 + 1.40 × 800 = Rs. 2800

Profit earned = 2800 - 2400 = Rs. 400 < 600
So, ‘II’ cannot be the answer.

For III:
Cost price of articles ‘A’ and ‘B’ together
= 1200 × 2 = Rs. 2400

Cost price of article ‘A’ = (2400 + 400)/2 = Rs. 1400
Cost price of article ‘B’ = 2400 - 1400 = Rs. 1000

Selling price of both articles = 0.90 × 1.75 × 1400 + 1.40 × 1000 = Rs. 3605

Profit earned = 3605 - 2400 = Rs. 1205 > 1200
So, ‘III’ cannot be the answer.

33. Rajan sold an article to Pankaj at __% profit. Pankaj repaired the article for Rs. 400 and sold it at a profit of __% such that the selling price of the article for Rajan is Rs. 800 less than that for Pankaj. Cost price of the article for Rajan is an integer.

The values given in which of the following options will fill the blanks in the same order in which is it given to make the statement true:

I. 20%, 25%
II. 25%, 20%
III. 40%, 80%

Correct Answer: (c) Only I and II
Solution:

Let the cost price of the article for Rajan be Rs. x

For I:
Selling price of the article for Rajan = Rs. 1.2x
Selling price of the article for Pankaj = 1.25(1.2x + 400) = Rs. (1.5x + 500)

According to the question,
1.5x + 500 - 1.2x = 800
0.3x = 300
x = 1000 (possible)

Therefore, I is true.

For II:
Selling price of the article for Rajan = Rs. 1.25a
Selling price of the article for Pankaj = 1.2(1.25a + 400) = Rs. (1.5a + 480)

According to the question,
1.5a + 480 - 1.25a = 800
0.25a = 320
a = 1280 (possible)

Therefore, II is true.

For III:
Selling price of the article for Rajan = Rs. 1.4p
Selling price of the article for Pankaj = 1.8(1.4p + 400) = Rs. (2.52p + 720)

According to the question,
2.52p + 720 - 1.4p = 800
1.12p = 80
p = 71.42 (not possible)

Therefore, III is false.

34. Aradhya bought a second hand scooty at a certain amount and made a down payment of Rs. 13800 and rest of amount in three equal quarterly installments of Rs. 26620 at the rate of 40% compound interest, then what is the price of the second hand scooty?

Correct Answer: (c) Rs. 80000
Solution:

Let Rs. S be the price of the scooty.

So, S - 13800 = 26620/(1 + 40/400) + 26620/(1 + 40/400)² + 26620/(1 + 40/400)³

=> S - 13800 = 66200
=> S = Rs. (66200 + 13800)
=> S = Rs. 80000

35. Rita bought two cellphones and sold them at the same price. She gained p% on one phone while suffered a loss of 16% on the other. The cost of the phone sold at loss was Rs. 2000 more than the other phone. Had she sold both at p% profit, she would have received a total of Rs. 11200. What was the total cost of the phones?

Correct Answer: (e) Rs. 8000
Solution:

Let the C.P. of the two phones be Q and Q - 2000.
Let Q + Q - 2000 = A (total cost price)
So, Q = A/2 + 1000

S.P. of the phone sold at loss = (100 - 16)/100 × Q
= 0.84Q

S.P. of the phone sold at profit = (100 + p)/100 × (Q - 2000)
= Q - 2000 + pQ/100 - 20p

As both the S.P. are equal, so 0.84Q = Q - 2000 + pQ/100 - 20p

84Q = 100Q - 200000 + pQ - 2000p
Q(16 + p) - 2000p = 200000

(A/2 + 1000)(16 + p) - 2000p = 200000

16A + pA + 32000 - 2000p + 4000p = 400000
16A + pA - 2000p = 368000 … (i)

For the second case:
(100 + p)/100 × A = 11200
100A + pA = 1120000 … (ii)

Solving (i) and (ii), we get
A = 8000 and p = 40

36. Mr. Rajan invested Rs 1,00,000 in UK Stock Markets when the GBPINR rate was 75. After one year his investment appreciated by 20% in GBP terms. He sold his investments and repatriated the money to India at the then existing rate of 80. What was real returns in INR?

Correct Answer: (b) gain of 28%
Solution:

Money invested by Rajan before 1 year was
= Rs. 100000

Money in UK pounds @ 75 is = 100000/75
= 1333.33 Pounds

Now, after 1 year invested amount was appreciated by 20%
=> 20% of 1333.33 = 266.66

Total investment becomes = 1333.33 + 266.66
= 1600 Pounds

This 1600 Pounds @ Indian currency at 80
= 1600 × 80 = Rs. 1,28,000

Hence, Rajan’s investment of Rs. 1,00,000 becomes Rs. 1,28,000 in 1 year

Therefore, his profit % = [(128000 - 100000)/100000] × 100 = 28%

37. The Maximum Retail Price (MRP) of a product is 55% above its manufacturing cost. The product is sold through a retailer, who earns 23% profit on his purchase price. What is the profit percentage for the manufacturer who sells his product to the retailer? The retailer gives 10% discount on MRP.

Correct Answer: (d) 13%
Solution:

Let the manufacturing cost = 100
The MRP of the product is 55% above its manufacturing cost
The MRP of the product = 100 + 55% of 100
= 155

The retailer sells the product after offering a discount of 10% on the MRP.
So, the retailer sells the product at 155 - 10% of 155 = 155 - 15.5 = 139.5

Let the purchase price for the retailer be x.
Therefore, the retailer sells the product at x + 23% of x = 123% of x.

Retailer sells the product at 139.5 = 123% of x
1.23x = 139.5
(or x = 139.5/1.23)

Therefore, x = 113.4

The manufacturer sold the product at 113.4.
Cost to the manufacturer is 100.

So, profit made by the manufacturer is 13.4.
Rounded to the nearest integer, is 13%.

38. If the selling price of an article is doubled, then its loss per cent is converted into equal profit per cent. The loss per cent on the article is?

Correct Answer: (b) 33 1/3%
Solution:

Let CP = C, SP = S, Loss% = x %

=> x = (C - S)/C × 100 ……… (1)

When SP is doubled, loss% becomes profit%.
x = (2S - C)/C × 100 ……… (2)

From eqns (1) and (2),
2S - C = C - S
3S = 2C => S = 2/3 C

Substituting S = 2/3 C in eqn (1),
x = (C - 2/3 C)/C × 100
= (C/3)/C × 100
= 100/3 = 33 1/3%

39. A dealer purchased a printing machine for Rs. 7660. He allows a discount of 12% on its marked price and still gains 10%. Find the marked price of the machine.

Correct Answer: (a) 9575
Solution:

Cost price of the machine = Rs. 7660, Gain% = 10%

Therefore, selling price = [(100 + gain%)/100] × CP
= [(100 + 10)/100] × 7660
= (110/100) × 7660 = Rs. 8426

Let the marked price be Rs. x.
Then, the discount = 12% of x
= (x × 12/100)
= 3x/25

Therefore, SP = (Marked Price) - (discount)
= (x - 3x/25)
= 22x/25

But, the SP = Rs. 8426.
Therefore, 22x/25 = 8426

=> x = (8426 × 25/22)
=> x = 9575

40. A person sold a toy for Rs. 136 and got 15% loss, had he sold it for Rs. N, he would have got a profit of 15%. Which one of the following is correct?

Correct Answer: (b) 180 < N < 190
Solution:

Cost price = (selling price × 100)/(100 - loss%)
= (136 × 100)/(100 - 15)
= (136 × 100)/85 = Rs. 160

Selling price (N) = 160 × (100 + 15)/100 = (160 × 115)/100 = Rs. 184