Question

Q.1) A sum of money is divided in the ratio 3:5. If the larger part is Rs 315, find the smaller part.
Q.2) A sum of money is divided between Marry and Jean in the ratio 4:7. If Jean's share is Rs. 595, find the total amount.
Q.3) Two numbers are in the ratio 5:8. If their difference is 48, find the number.
Q.4) A certain sum of money is divided into three parts in the ratio 5:7:8. If the first part is Rs.225, find the total amount and the other two parts.

Answer 1

1) Sum of the ratio = 3 + 5 = 8
5/8 of x = 315
5x = 315 * 8
5x = 2520
x = 2520/5
= Rs 504
Total money = Rs 504
3/8 * 504 = Rs 189
The smaller part is Rs 189.
2) Sum of the ratio = 4 + 7 = 11
7/11 of x = 595
7x = 595 * 11
7x = 6545
x = 6545/7
x = Rs 935
Total money = Rs 935
3) 8x - 5x = 48
3x = 48
x = 48/3
x = 16
5x = 16 * 5 = 80
8x = 16 * 8 = 128
The 2 numbers are 128 and 80.
4) Sum of the ratios = 5 + 7 + 8 = 20
5/20 of x = 225
5x = 225 * 20
5x = 4500
x = 4500/5
x = Rs 900
Total money = Rs 900
7/20 * 900 =  Rs 315
8/20 * 900 = Rs 360
The total money is Rs 900. The other 2 parts are Rs 315 and Rs 360.

Answer 2

1)      Smaller : Bigger = 3 : 5            Smaller / Bigger = 3 / 5

             Smaller = bigger * 3 / 5 = Rs 315 * 3 / 5 = Rs 189

2)  Mary / Jean = 4 / 7 

            Mary = Jean * 4 / 7  =  Rs 595 * 4 / 7  = Rs 340

             Total = Rs 595 + 340 = Rs 935

3)
 $\frac{M}{ N} = 5 / 8 \\ \\ M = \frac{N * 5}{ 8} \\ \\ N - M = N - N * 5/8 = N * (1 - \frac{5}{ 8} ) = N * \frac{3}{8} \\ \\ N - M = 48 = N * 3/8 \\ \\ N = 48 * 8 / 3 = 128 \\ \\ M = 128 - 48 = 80$

4)  P : Q : R  = 5 : 7 : 8          Let P = 5 x    Q = 7 x      R = 8 x
     P = 5 x = Rs 225      x = 225/5  = Rs  45
     Total = 5x + 7x + 8 x = 20 x = 20 * 45 = Rs 900