Ratio and Proportion MCQs

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.

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A. 96
B. 68
C. 72
D. 108
✅ The correct answer is option D. 108.
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

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?

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A. 120
B. 80
C. 192
D. 48
✅ The correct answer is option D. 48.
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

A bag contains 1 rupee, 2 rupee and 5 rupee coins amounting to Rs.264. If the ratio of the number of these coins is 3:5:4, find the number of 1 rupee coins.

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A. 66
B. 48
C. 24
D. 8
✅ The correct answer is option C. 24.
Let the number of 1 rupee, 2 rupee and 5 rupee coins be 3x, 5x and 4x. (1*3x)+(2*5x)+(5*4x)=264 3x+10x+20x=264 33x=264 x=8 No. of 1 rupee coins

= 3x = 24

The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is :__________?

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A. 20
B. 30
C. 48
D. 58
✅ The correct answer is option B. 30.
Let the three parts be A, B, C Then,

A : B = 2 : 3 and B : C = 5 : 8 (5 X 3/5 ) : (8 X 3/5 ) = 3 : 24/5

A:B:C= 2 : 3 : 24/5 10:15:24

B = (98 X 15/49 ) = 30.

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.

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A. 16 : 2 : 3
B. 8 : 3 : 6
C. 16 : 2 : 9
D. 6 : 9 : 1
✅ The correct answer is option C. 16 : 2 : 9.
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