Q1. If the cost price of 12 articles be equal to the selling price of 10 articles, then find the profit per cent in the transaction.
(a) 15
(b) 20
(c) 25
(d) Data insufficient
Sol.
Let the CP of 1 articles = Rs. 1
Then, CP of 12 articles = Rs. 12 = SP of 10 articles
Also, CP of 10 articles = Rs. 10
Profit percent =(2/10×100)%=20%
Q2. A grocer purchased 75 kg of sugar at Rs. 30 per kg and mixed it with 25 kg of sugar at Rs. 36 per kg. At what rate should he sell the mixture to gain 10%?
(a) Rs. 32.20
(b) Rs. 32.45
(c) Rs. 32.60
(d) None of these
Sol.
CP of 100 kg of mixture = (75 × 30 + 25 × 36) = Rs. 3150
SP = 110% of 3150 =(110/100×3150) = Rs. 3465
Rate of SP of the mixture =(3465/100) = Rs. 34.65
Q3. Rehaan purchased a bike for Rs. 54000. He sold it at a loss of 8%. With that money he again purchased another bike and sold it at a profit of 10%. What is his overall loss/profit?
(a) Loss of Rs. 657
(b) Profit of Rs. 567
(c) Loss of Rs. 648
(d) Profit of Rs. 648
Sol.
Cost price = Rs. 54000
Selling price = 54000×((100-8))/100 = Rs. 49680
Now, the cost price of another bike = Rs. 49680
Selling price of another bike = 49680×110/100 = Rs. 54648
Overall profit = 54648 – 54000 = Rs. 648
Q4. 6 bells commence tolling together and toll of intervals are 2, 4, 6, 8, 10 and 12 s, respectively. In one hour, how many times do they toll together?
(a) 16
(b) 32
(c) 21
(d) 31
Sol.
LCM of 2, 4, 6, 8, 10, 12 = (2 × 2 × 3 × 2 × 5) = 120
∴ After every 2 min they toll together
∴ Number of times they toll together in one hour
=(60/2+1) times = 31 times
Q5. A certain type of board is sold in lengths of multiples of 2 ft. the shortest board sold is 6 ft and the longest is 24 ft. A builder needs a large quantity of these types of board in 5 1/2 ft lengths. Find the length of be ordered for which waste is minimum.
(a) 24 ft
(b) 26 ft
(c) 22 ft
(d) 52 ft
Sol.
LCM of (2 and 5 1/2) = LCM of (2 and 11/2)
Required answer =(LCM of 2 and 11)/(HCF of 1 and 2)=22/1 = 22 ft
Q6. The average expenditure of a man for the first 12 days of a month was Rs. 850 per day and for the next 18 days, it was Rs. 825 per day. If he could save Rs. 700 during that month. Find his income for the month.
(a) Rs. 22650
(b) Rs. 29450
(c) Rs. 24150
(d) Rs. 25750
Sol.
Expenditure for the first 12 days (850 × 12) = Rs. 10200
Expenditure for the next 18 days = (825 × 18) = Rs. 14850
Savings = Rs. 700
∴ Income for the month = (10200 + 14850 + 700) = Rs. 25750
Q7. A company employed 600 men and 400 women, their average wage was Rs. 68 per day. If a woman gets Rs. 30 less than a man, what is the average wage of a woman?
(a) Rs. 50
(b) Rs. 51
(c) Rs. 54
(d) Cannot be determined
Sol.
Let the average wage of a man = Rs. x
Then, the average wage of a woman = Rs. (x – 30)
Now, (600 × x + 400(x – 30) )/(600 + 400)=68
⇒ 600x + 400(x – 30) = 68000
⇒ 6x + 4(x – 30) = 680
⇒ 10x = 800
⇒ x=800/10=80
Thus, the average wage of woman = (80 – 30) = Rs. 50
Q8. A sum of money is divided among A, B, C and D in the ratio of 2 : 7 : 11 : 12. If the share of B and D together is Rs. 6650, then what is the difference between the amounts of A and D?
(a) Rs. 3600
(b) Rs. 3500
(c) Rs. 3800
(d) Cannot be determined
Sol.
Let the share of A, B, C and D be 2x, 7x, 11x and 12x, respectively.
Then, B + D = (7x + 12x) = 19x = 6650
⇒ x = 350
Now, D – A = (12x – 2x) = 10x = (10 × 350) = Rs. 3500
Q9. In a class of 45 students, the ratio of boys and girls is 2 : 3. How many more boys are to be added to make the ratio 1 : 1?
(a) 6
(b) 12
(c) 15
(d) None of these
Sol.
The number of boys =2/5×45 = 18 boys
The number of girls =3/5×45 = 27 girls
Now, when 9 more boys are added the new ratio becomes = 27 : 27 = 1 : 1
∴ 9 more boys are to be added.
Q10. The ratio of the present age of Manoj to that of Wasim is 3 : 11. Wasim is 12 yr younger than Rehana. Rehana’s age after 7 yr will be 85 yr. What is the present age of Manoj’s father, who is 25 yr older than Manoj?
(a) 61 yr
(b) 67 yr
(c) 43 yr
(d) 49 yr
Sol.
Let the present ages of Manoj and Wasim are 3x yr and 11x yr, respectively.
According to the question, 11x = 85 – 7 – 12
⇒ 11x = 66
∴ x = 6
∴ Present age of Manoj = 3 × 6 = 18 yr
Hence, present age of Manoj’s father = 18 + 25 = 43 yr
