Ratio and Proportion Problems and Solutions for SSC and Bank Exams

Ratio and Proportion Problems and Solutions for Competitive Exams

Q.6. A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7: 2 and 7 : 11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in  C will be :

Solution: 

$$Gold \ in \ C =   \left({7\over9}+ {7\over18}\right) \ Unit ={7\over6} \ units$$

  $$Copper \ in \ C =  \left({2\over9}+ {11\over18}\right)=units ={5\over6}\ units$$

  $$Gold : Copper ={7\over6}:{5\over6}=7:5  $$

Q.7. Which of the following ratios is greatest?

(A) 5: 7

(B) 15: 23

(C) 17: 25

(D) 21: 29

Solution: 

$${7\over15}=0.466,\ {15\over23}=0.652, \ {17\over25}=0.68 \ and \ {21\over29}=0.724   $$

  Clearly, 0.724 is greatest and therefore, 21 : 29 is greatest.

Q.8. A certain amount was divided between A and B in the ratio 4 : 3. If B’s share was Rs. 4800, the total amount was :

Solution: 

If B’s share is Rs. 3, total amount = Rs. 7.

Of B’s share is Rs. 4800,   $$Total \ amount=Rs. \left({7\over3}× 4800\right)=Rs.11200.$$

Q.9. A sum of Rs. 53 is divided among A, B, C in such a way that A gets Rs. 7 more than what B gets and B gets Rs. 8 more than what C gets. The ratio of their shares is :

Solution:

Suppose C gets Rs. x. Then, B gets Rs.(x+8) and A gets Rs.(x+15).

Then, x+(x+8) +(x+15) = 53 ↔ x=10.

∴ A : B : C = (10+15): (10+8):10=25:18:10.

Q.10. What is the ratio whose terms differ by 40 and the measure of which is ?

Solution:

Let the ratio be x : (x+40). Then,

$$ \left({x\over(x+40)}=\right) {2\over7}=7x=2x+80↔x=16.$$

∴ Required ratio = 16 : 56

For more Ratio and Proportion questions and answers, Visit next page..