Problems on Ratio and Proportion PART-2

6: Rs 1210 were divided among three-person P, Q, R so that P: Q = 5: 4 and Q: R = 9: 10. Then R gets the amount.

A. 450

B. 400

C. 500

D. 375

E. None of these

7: Share Rs.4200 among joy, Sanjay, and joy in the ration 2: 4: 6.Find the amount received by Sanjay.

A. 1200

B. 1300

C. 1400

D. 1500

E. None of these

8 : Find the mean proportional between given two number that is 64 and 49.

A. 45

B. 52

C. 54

D. 56

E. None of these

9: What number has to be added to each term of 3: 5 to make the ratio 5: 6.

A. 7

B. 6

C. 8

D. 5

E. None of these

10: Rs. 385 were divided among P, Q, R in such a way that P had Rs 20 more than Q and R had Rs 15 more than P. How much was R’s share?

A. 156

B. 145

C. 152

D. 150

E. None of these

Solutions :

6. P : Q = 5 : 4, Q : R = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9.

So, P : Q : R = 5 : 4 : 40 /9 = 45 : 36 : 40
Sum of ratio terms is = ( 45 + 36 + 40 ) =121.
R share of amount is Rs (1210 x 40 / 121) = Rs. 400.

7. The amount received by Sanjay.
4 / 12 X 4200 = 1400= ( related ratio / sum of ratio ) x Total amount
So, the Amount received by Sanjay is 1400.

8. The mean proportion of two numbers is
Root of 64 and 49 is √8 x √ 7 = 8 x 7 = 56.
So, the mean proportional is 56.

9.Let the number to be added x , Then
3 + x / 5 + x = 5 / 6
6 ( 3 + x ) = 5 ( 5 + x )
x = ( 25 – 18 ) = 7
So , the number to be added is 7 .

10. Let Q gets Rs x. Then We can say P gets Rs (x + 20 ) and R gets Rs ( x + 35) .
x + 20 + x + x + 35 = 385
3x = 330
x = 110 .
R’s share = Rs ( 110 + 35 ) = Rs 145 .