**Q1. The average of the first 100 positive integers is:**

(a) 100

(b) 51

(c) 50.5

(d) 49.5

**S1. Ans.(c)**

**Sol.** The required average = (1+2+⋯……….. 100)/100

= (100 × 101)/(2 × 100) = 50.5

**Q2. The average marks scored by Ganesh in English, Science, Mathematics and History is 15 marks less than what he scored in English, History, Geography and Mathematics. What is the difference of marks in Science and Geography, Ganesh scored?**

(a) 40

(b) 50

(c) 60

(d) Data inadequate

**S2. Ans.(c)**

**Sol.** (E + S + M + H)/4-(E + H + G + M)/4 = 15

or, E + S + M + H – E – H – G – M = 60

∴ S – G = 60.

**Q3. The average marks of 14 students was calculated as 71. But, it was later found that the marks of one student had been wrongly entered as 42 instead of 56 and of another as 74 instead of 32. The correct average is:**

(a) 67

(b) 68

(c) 69

(d) 71

**S3. Ans.(c)**

**Sol.** Marks obtained by 14 students

= 14 × 71 = 994

Exact marks of 14 students

= 994 + {(56 – 42) + (32 – 74)}

= 994 + {14 + (–42)} = 994 + {–28}

= 994 – 28 = 966

∴ Correct average = 966/14 = 69.

**Q4. Average weight of three boys P, T and R is 54(1/3) kg while the average weight of three boys T, F and G is 53 kg. What is the average weight of P, T, R, F and H?**

(a) 53.8 kg

(b) 52.4 kg

(c) 53.2 kg

(d) Data inadequate

**S4. Ans.(d)**

**Sol.** We are to determine the average weight of P, T, R, F and H.

Obviously, this cannot be determined as we do not know the weight of H.

**Q5. The average of four positive integers is 72.5. The highest integer is 117 and the lowest integer is 15. The difference between the remaining two integers is 12. Which is the higher of these two remaining integers?**

(a) 73

(b) 84

(c) 70

(d) None of these

**S5. Ans.(d)**

**Sol.** We have, 117 + x + (x + 12) + 15 = 72.5 × 4

[where x is the lower integer among the remaining two integers]

⇒ 2x = 290 – 144

∴ x = 73

Hence the higher integer (among the remaining two integers)

= 73 + 12 = 85

**Q6. The average weight of 8 persons increases by 1.5 kg. If a person weighting 65 kg is replaced by a new person, what could be the weight of the new person?**

(a) 76 kg

(b) 77 kg

(c) 76.5 kg

(d) Data inadequate

**S6. Ans.(b)**

**Sol. **weight of the new person=8 × 1.5 +65=77kg

**Q7. Kamya purchased an item for Rs. 46,000 and sold it at a loss of 12 percent. With that amount she purchased another item which he sold at a gain of 12%. What was her overall gain/loss?**

(a) Loss of Rs. 662.40

(b) Profit of Rs. 662.40

(c) Loss of Rs. 642.80

(d) Profit of Rs. 642.80

**S7. Ans.(a)**

**Sol.** First S.P. = (46000 × 88)/100 = Rs. 40480

Second S.P. = (40480 × 112)/100 = Rs. 45337.6

∴ Loss = Rs. (46000 – 45337.6) = Rs. 662.4

**Q8. A merchant purchases a wrist watch for Rs. 450 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. Then the list price (in rupees) of the wrist watch is:**

(a) Rs. 500

(b) Rs. 600

(c) Rs. 750

(d) Rs. 800

**S8. Ans.(b)**

**Sol. **Let, the list price of wrist watch be Rs. x.

Selling price of wrist watch at 10% discount

=Rs.x((100-10)/100)=Rs.9x/10

Cost price of wrist watch at 20% profit

= Rs. 9x/10 (100/(100 + 20)) = Rs. (9x/10×10/12) = Rs. 3x/4

Now, according to the question,

3x/4 = 450 ⇒ x = (450 × 4)/3 = 600

∴ List price of the wrist watch = Rs. 600

**Q9. By selling an article for Rs. 21, a man lost such that the percentage loss was equal to the cost price. The cost price of the article was:**

(a) Rs. 30 or Rs. 70

(b) Rs. 35 or Rs. 60

(c) Rs. 45

(d) R. 50

S9. Ans.(a)

Sol. Let, the cost of article be Rs. x.

At x% loss, the article sold at Rs. 21.

Now, according to the question,

x((100-x)/100) = 21 ⇒ x(1-x/100) = 21

⇒ x-x^2/100 = 21 ⇒ x^2- 100x + 2100 = 0

⇒ (x – 30)(x – 70) = 0

∴ x = Rs. 30 or, Rs. 70

**Q10. A sells an article to B at a gain of 25%, B sells it to C at a gain 20% and C sells it to D at a gain of 10%. If D pays Rs. 330 for it, how much did it cost A?**

(a) Rs. 200

(b) Rs. 250

(c) Rs. 275

(d) Rs. 290

**S10. Ans.(a)**

**Sol. **Let, A buy the article in Rs. 100.

According to the question,

B’s cost = Rs. 125

C’s cost = Rs. 125((100 + 20)/100) = Rs. 150

D’s cost = Rs. 150((100 + 10)/100) = Rs. 165

Here, at the end the article was sold out at Rs. 165.

∴ Required cost for A = 330/165 × 100 = Rs. 200.

**Q11. A man had a certain amount with him. He spent 20% of that to buy an article and 5% of the remaining on transport. Then he gifted Rs. 120. If he is left with Rs. 1,400, the amount he spent on transport is:**

(a) Rs. 76

(b) Rs. 61

(c) Rs. 95

(d) Rs. 80

**S11. Ans.(d)**

**Sol.** Let, the total amount be Rs. x

Now, according to the question,

∴ x – x/5-4x/5×5/100 – 120 = 1400

⇒ x – x/5-x/25 = 1520

⇒ (25x – 5x – x)/25 = 1520

⇒ 19x/25 = 1520

⇒ x = (1520 × 25)/19 = Rs. 2000

∴ Expenditure on transport

=4x/5×5/100=x/25=1/25×2000

= Rs. 80

**Q12. A shopkeeper marks his goods at 40% above their cost price. He is able to sell 3/4th of his goods at this price, and the remaining at 40% discount. Assuming that the shopkeeper is able to sell the goods he buys, find his loss or gain as % of the whole transaction.**

(a) 20% loss

(b) 23% loss

(c) 26% gain

(d) 30% gain

**S12. Ans.(c)**

**Sol.** Total C.P. = Rs. 100 (100 articles)

Total S.P. = 75 × 140/100 + 25 × 60/100 × 1.4

= 105 + 21 = Rs. 126

∴ Gain percent = 26

**Q13. A shopkeeper buys 144 items at 90 paisa each. On the way 20 items are broken. He sells the remainder at Rs. 1.20 each. His gain percent correct to one place of decimal is:**

(a) 13.8%

(b) 14.6%

(c) 14.8%

(d) 15.8%

**S13. Ans.(c)**

**Sol. **20 items are broken out of 144 items.

∴ C.P. of 124 items

= Rs. ((144 × 90)/100) = Rs. 129.60

Total S.P. = Rs. (1.20 × 124) = Rs. 148.8

∴ Gain = Rs. (148.80 – 129.60) = Rs. 19.20

∴ Gain percent = 19.20/129.60 × 100 = 14.8%

**Q14. By selling an article for Rs. 144, a person gained such that the percentage gain equals the cost price of the article. The cost price of the article is:**

(a) Rs. 90

(b) Rs. 80

(c) Rs. 75

(d) Rs. 60

**S14. Ans.(b)**

**Sol.** Let, the C.P. of the article be Rs. x.

Then,

(144 – x)/x × 100 = x

⇒ (144 – x) × 100 = x^2

⇒ x^2 + 100x – 14400 = 0

⇒ x^2 + 180x + 80x – 14400 = 0

⇒ x (x + 180) – 80 (x + 180) = 0

⇒ (x – 80) (x + 180) = 0

Therefore, x = Rs. 80

**Q15. A businessman marks his goods in such a way that even after allowing 12.5% discount on cash purchase, he gains 20%. If the cost price of the goods is Rs. 140, the marked price is:**

(a) Rs. 162

(b) Rs. 172

(c) Rs. 192

(d) Rs. 198

**S15. Ans.(c)**

**Sol. **Suppose marked price = Rs. K

∴ K – 12.5% of K = 140 + 20% of 140

⇒ 87.5% of K = 140 + 28 = 168

∴ K = 16800/87.50 = 192.