651. The ratio of two numbers a and b is 3:5. If 2 is added to both the numbers, the ratio becomes 2:3. Find b.
A. 15
B. 10
C. 8
D. 5

Explanation
a:b = 3:5 5a = 3b (a+2):(b+2) = 2:3 3(a+2) = 2(b+2) 3a+6 = 2b+4 3*(3b/5) = 2b-2 9b = 10b-10 b =10

652. The plan for a rectangular area is drawn to a scale of 1:500. If the length and breadth in the plan is 30 cm and 20 cm, find the actual area.
A. 1200 m²
B. 1500 m²
C. 12000 m²
D. 15000 m²

Explanation:
Actual length
= 30*500 cm Actual breadth
= 20*500 cm Actual area
= 30*20*500*500 = 15000 m²

653. The length and breadth of a rectangle are in the ratio 5:4. Find its perimeter if its area is 180 cm²
A. 54 cm
B. 27 cm
C. 12 cm
D. 15 cm

Explanation:
Let the length and breadth be 5x cm and 4x cm.
5x*4x=180
20x²=180
x²=9,x=3 Length = 15cm Breadth = 12cm Perimeter
= 2(l+b)
= 2*27
= 54 cm

654. In what ratio should the profit of Rs.8000 be divided if X starts a business with an investment of Rs. 20000, Y invests Rs.7500 for 4 months and Z invests Rs.15000 after 3 months from the start of the business.
A. 16 : 2 : 3
B. 8 : 3 : 6
C. 16 : 2 : 9
D. 6 : 9 : 1

Explanation:
Let the profit of X be P1, that of Y be P2 and of Z be P3.
P1:P2:P3 = 20000*12 : 7500*4 : 15000*9 = 240 : 30 : 135 = 80 : 10 : 45
= 16 : 2 : 9

655. M:N = 3:4, N:O = 5:7 and O:P = 7:9. Then M:P =________?
A. 1/3
B. 7/9
C. 5/12
D. None of these

Explanation:
M/P = M/N * N/O * O/P = ¾ * 5/7 * 7/9 = 5/ 12

656. The perimeter of a triangle is 81 cm. If the sides are in the ratio 4:3:2, find the length of the largest side.
A. 45 cm
B. 40 cm
C. 36 cm
D. 27 cm

Explanation:
Let the three sides be 4x,3x and 2x. 4x+3x+2x = 81 9x = 81 x = 9 Length of the largest side
= 4x = 36 cm

657. The ratio of boys and girls in a class was 11:13. 8 girls and 4 boys join the class from this academic year and the ratio becomes 4:5. Find the strength of the class.
A. 96
B. 68
C. 72
D. 108

Explanation:
Let the number of boys and girls in the class be 11x and 13x. 4 boys and 8 girls join the class. Strength of the class
= 11x+13x+4+8
= 24x+12 (11x+4):(13x+8) = 4:5 5*(11x+4)=4*(13x+8) 55x+20=52x+32 3x=12 x=4 24x+12=108

658. A class has 90 students. If the ratio of boys and girls is 7:8, find the number of boys in the class.
A. 48
B. 42
C. 60
D. 70

Explanation:
7x+8x=90 15x=90 x=6 Number of boys=7x=42

659. In a partnership for a business, Changaz invests Rs.6000 for complete year & Nasir invests Rs.3000 for 6 months. What is Nasir’s share if they earn Rs.240 as profit?
A. 120
B. 80
C. 192
D. 48

Explanation:
If A invests amount C1 for T1 time and his share of profit is P1, and B invests amount C2 for T2 time and his share of profit is P2, then, C1 * T1 / C2 * T2 = P1/P2
If P is the Nasir’s share of profit, then Changaz gets (240 – P)
Therefore, 6000 * 12 / 3000 * 6 = (240 – P) / P = 72/ 18 = 4
4P = (240 – P)
5P = 240
P = 48

660. If x% of 200=y% of 250, find y:x.
A. 5:4
B. 5:2
C. 2:5
D. 4:5

Explanation:
(x/100)*200 = (y/100)*250 y/x = 20/25 = 4/5 y:x=4:5

NOTE
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