Questions:
1. The ratio of the no. of boys to the no. of girls in a school of 720 students is 3: 5. If 18 new girls are admitted in the school, find how many new boys may be admitted so that the ratio of the no. of boys to the no. of girls may change to 2 : 3.
A) 80
B) 50
C) 42
D) 35
E) None of these
A) (4p, –3p)
B) (4p, 3p)
C) (–4p, 3p)
D) (–4p, –3p)
E) None of these.
3. What is the amount of compound interest and effective rate of interest if an amount of Rs.20000 is deposited in a bank for one year at the rate of 8% per annum compounded semi annually.
A) 1632, 8.16%
B) 1600, 9.36%
C) 1936, 10.36%
D) 1756, 9.56%
E) None of these.
4. 3 men can complete a piece of work in 6 days. Two days after they started the work, 3 more men joined them. How many days will they take to complete the remaining work?
A) 5 days
B) 2 days
C) 8 days
D) 12 days
E) None of these.
5. Two pipes A and B can fill a tank in 36 min. and 45 min. respectively. A water pipe C can empty the tank in 30 min. First A and B are opened. After 7 minutes, C is opened. In how much time, the tank is full?
A) 45 minutes
B) 46 minutes
C) 52 minutes
D) 56 minutes
E) None of these.
6. Abhishek purchased 140 shirts and 250 trousers at the rate of Rs. 450 and Rs. 550 respectively. What should be the overall average selling price of shirts and trousers so that 40% profit is earned? (Rounded off to next integer).
A) Rs.725
B) Rs.710
C) Rs. 720
D) Rs. 700
E) None of these
7. In a college the students in Arts and Commerce faculties were in the ratio of 4:5 respectively. When 65 more students joined Commerce faculty the ratio became 8:11 respectively. How many students are there in Arts faculty?
A) 520
B) 650
C) 715
D) Cannot be determined
E) None of these
8. An amount of Rs. 10,000 becomes Rs. 14,641 in two years if the interest is compounded half yearly. What is the rate of compound interest % per annum?
A) 10
B) 20
C) 16
D) 12
E) None of these
Answers with solutions:
1.(C) The ratio of the no. of boys to the no. of girls = 3 : 5
Sum of the ratios = 3 + 5 = 8
So, the no. of boys in the school = (3 × 720)/8 = 270
And the no. of girls in the school = (5 × 720)/8 = 450
Let the no. of new boys admitted be x, then the no. of boys become (270 + x).
After admitting 18 new girls, the no. of girls become 450 + 18 = 468
According to given description of the problem, (270 + x)/468 = 2/3
or, 3 (270 + x) = 2 x 468
or, 810 + 3x = 936 or, 3x = 126 or, x = 42.
Hence the no. of new boys admitted = 42.
2.(A) 7(x+2p)^2+5p^2= 35px+117 p^2
7x^2+33p^2+28px = 35px+ 117 p^2
x^2-px+12p^2 = 0
on solving x= 4p,-3p
3.(A) Interest = 20000[(1+4/100)^2-1]= 1632
Efeective rate of interst = 1632/20000*100= 8.16%
4.(B) Work done by 3 men in 2 days = (1/6x 2 )=1/3.
Remaining work = (1 – 1/3)= 2/3
Now 3 men's 1 day's work =1/6
1 man's 1 day's work = 1/18
6 men's 1 day's work = (6 x 1/18=1/3
Now, 1/3 work is done by them in 1 day.
2/3 work is done by them in (3 x2/3)= 2 days.
5.(B) Part filled in 7 min = 7[ 1/36 + 1/45] = 7/20
Remaining part = [ 1- 7/20] = 13/20
Net part filled in 1 min. When A,B and C are opened
= [ 1/36 + 1/45 + 1/30 ] = 1/60
Now, 1/60 part is filled in 1 min.
13/20 part is filled in [60x13/20] = 39 min
Total time taken to fill the tank = (39 + 7) min. = 46 min.
6. (C); CP of 140 shirts and 250 trousers
= Rs (140 * 450 + 250 * 550)
= Rs. (63000 + 137500) = Rs 200500
SP for 40% profit = Rs (140/100 ×200500)=280700
Average selling price = Rs (280700/(140+250) )=Rs.720
7. (A): Let the initial number of students in Arts and Commerce faculties be 4x and 5x respectively.
According to the question,
4x/(5x+65)=8/11
44x = 40x + 520
= x = 520/4 = 130
Number of students in Arts faculty = 4 * 130 = 520
8. (B) Time = 4 half years
Rate = R% per half year
A = P (1+R/100)^T
14641 = 10000 (1+R/100)^4
(1+R/100)^4 = 14641/10000= (11/10)^4
1+R/100=11/10 ? R/100=1/10
R =10%
Rate % per annum = 20%
1.(C) The ratio of the no. of boys to the no. of girls = 3 : 5
Sum of the ratios = 3 + 5 = 8
So, the no. of boys in the school = (3 × 720)/8 = 270
And the no. of girls in the school = (5 × 720)/8 = 450
Let the no. of new boys admitted be x, then the no. of boys become (270 + x).
After admitting 18 new girls, the no. of girls become 450 + 18 = 468
According to given description of the problem, (270 + x)/468 = 2/3
or, 3 (270 + x) = 2 x 468
or, 810 + 3x = 936 or, 3x = 126 or, x = 42.
Hence the no. of new boys admitted = 42.
2.(A) 7(x+2p)^2+5p^2= 35px+117 p^2
7x^2+33p^2+28px = 35px+ 117 p^2
x^2-px+12p^2 = 0
on solving x= 4p,-3p
3.(A) Interest = 20000[(1+4/100)^2-1]= 1632
Efeective rate of interst = 1632/20000*100= 8.16%
4.(B) Work done by 3 men in 2 days = (1/6x 2 )=1/3.
Remaining work = (1 – 1/3)= 2/3
Now 3 men's 1 day's work =1/6
1 man's 1 day's work = 1/18
6 men's 1 day's work = (6 x 1/18=1/3
Now, 1/3 work is done by them in 1 day.
2/3 work is done by them in (3 x2/3)= 2 days.
5.(B) Part filled in 7 min = 7[ 1/36 + 1/45] = 7/20
Remaining part = [ 1- 7/20] = 13/20
Net part filled in 1 min. When A,B and C are opened
= [ 1/36 + 1/45 + 1/30 ] = 1/60
Now, 1/60 part is filled in 1 min.
13/20 part is filled in [60x13/20] = 39 min
Total time taken to fill the tank = (39 + 7) min. = 46 min.
6. (C); CP of 140 shirts and 250 trousers
= Rs (140 * 450 + 250 * 550)
= Rs. (63000 + 137500) = Rs 200500
SP for 40% profit = Rs (140/100 ×200500)=280700
Average selling price = Rs (280700/(140+250) )=Rs.720
7. (A): Let the initial number of students in Arts and Commerce faculties be 4x and 5x respectively.
According to the question,
4x/(5x+65)=8/11
44x = 40x + 520
= x = 520/4 = 130
Number of students in Arts faculty = 4 * 130 = 520
8. (B) Time = 4 half years
Rate = R% per half year
A = P (1+R/100)^T
14641 = 10000 (1+R/100)^4
(1+R/100)^4 = 14641/10000= (11/10)^4
1+R/100=11/10 ? R/100=1/10
R =10%
Rate % per annum = 20%
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